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Questions and Answers
Solve the equation: 4 + 8n = 6n + 8
Solve the equation: 4 + 8n = 6n + 8
n = 2
Solve the equation: 9x - (5x + 5) = 7x - 41
Solve the equation: 9x - (5x + 5) = 7x - 41
x = -18
Solve the equation: 3/7 -x - 2 = -x/4 - 2
Solve the equation: 3/7 -x - 2 = -x/4 - 2
x = 4
Solve the inequality: -6x + 8 ≤ 38. Express the solution using set-builder notation. The solution set is {x | x ______ -5}.
Solve the inequality: -6x + 8 ≤ 38. Express the solution using set-builder notation. The solution set is {x | x ______ -5}.
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Solve the inequality: -6x + 8 ≤ 38. Express the solution using interval notation. The solution set is [blank]
Solve the inequality: -6x + 8 ≤ 38. Express the solution using interval notation. The solution set is [blank]
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Solve the inequality: -4(x + 2) < 16. Express the solution using set notation. The solution is expressed in set notation as {x | x ______ -6}.
Solve the inequality: -4(x + 2) < 16. Express the solution using set notation. The solution is expressed in set notation as {x | x ______ -6}.
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Solve the inequality: -4(x + 2) < 16. Express the solution using interval notation. The solution is expressed in interval notation as [blank]
Solve the inequality: -4(x + 2) < 16. Express the solution using interval notation. The solution is expressed in interval notation as [blank]
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Solve the inequality: 0.5x - 15 ≤ 6. Express the solution using set notation. The solution is expressed in set notation as {x | x ______ 22}.
Solve the inequality: 0.5x - 15 ≤ 6. Express the solution using set notation. The solution is expressed in set notation as {x | x ______ 22}.
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Solve the inequality: 0.5x - 15 ≤ 6. Express the solution using interval notation. The solution is expressed in interval notation as [blank]
Solve the inequality: 0.5x - 15 ≤ 6. Express the solution using interval notation. The solution is expressed in interval notation as [blank]
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How much pure acid should be mixed with 6 gallons of a 60% acid solution to get a 70% acid solution?
How much pure acid should be mixed with 6 gallons of a 60% acid solution to get a 70% acid solution?
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The manager of a coffee shop has one type of coffee that sells for $10 per pound and another type that sells for $13 per pound. The manager wishes to mix 90 pounds of the $13 coffee to get a mixture that will sell for $12 per pound. How many pounds of the $10 coffee should be used?
The manager of a coffee shop has one type of coffee that sells for $10 per pound and another type that sells for $13 per pound. The manager wishes to mix 90 pounds of the $13 coffee to get a mixture that will sell for $12 per pound. How many pounds of the $10 coffee should be used?
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The manager of a candy shop sells chocolate covered peanuts for $5 per pound and chocolate covered cashews for $9 per pound. The manager wishes to mix 30 pounds of the cashews to get a cashew - peanut mixture that will sell for $8 per pound. How many pounds of peanuts should be used?
The manager of a candy shop sells chocolate covered peanuts for $5 per pound and chocolate covered cashews for $9 per pound. The manager wishes to mix 30 pounds of the cashews to get a cashew - peanut mixture that will sell for $8 per pound. How many pounds of peanuts should be used?
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Verify that the values of the variables listed are solutions of the system of equations: 3x + y = 15
4x + 3y = 30
x = 3, y = 6
Verify that the values of the variables listed are solutions of the system of equations: 3x + y = 15 4x + 3y = 30 x = 3, y = 6
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Verify that the values of the variables listed are solutions of the system of equations: 4x + y = -3
3x + 4y = 14
x = -2, y = -5
Verify that the values of the variables listed are solutions of the system of equations: 4x + y = -3 3x + 4y = 14 x = -2, y = -5
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Find the distance d(P1,P2) between the points P1 and P2: P1 = (3,3); P2 = (3, -5)
Find the distance d(P1,P2) between the points P1 and P2: P1 = (3,3); P2 = (3, -5)
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Find the midpoint of the line segment joining the points P1 and P2: P1 = (-6,6); P2 = (-9, -6)
Find the midpoint of the line segment joining the points P1 and P2: P1 = (-6,6); P2 = (-9, -6)
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Find the midpoint of the line segment joining the points P1 and P2: P1 = (7,1) ; P2 = (-16, -16)
Find the midpoint of the line segment joining the points P1 and P2: P1 = (7,1) ; P2 = (-16, -16)
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Determine whether the point (8,8) is on the graph of the equation: x² - y² = 64
Determine whether the point (8,8) is on the graph of the equation: x² - y² = 64
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List the intercepts and type(s) of symmetry, if any: y² = x + 1
List the intercepts and type(s) of symmetry, if any: y² = x + 1
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List the intercepts and type(s) of symmetry, if any: 16x² + y² = 16
List the intercepts and type(s) of symmetry, if any: 16x² + y² = 16
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Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin: x² + y - 1 = 0
Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin: x² + y - 1 = 0
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Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin: 16x² + y² = 16
Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin: 16x² + y² = 16
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Determine whether the given points are on the graph of the equation: y² = x² + 256. Points (0,16), (16,0), (-16, 0)
Determine whether the given points are on the graph of the equation: y² = x² + 256. Points (0,16), (16,0), (-16, 0)
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Determine which of the given points are on the graph of the equation: x² + y² = 4. Points: (2,0), (-2,2), (√2, √2)
Determine which of the given points are on the graph of the equation: x² + y² = 4. Points: (2,0), (-2,2), (√2, √2)
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Plot the point (-2, 3). Then plot the point that is symmetric to it with respect to (a) the x-axis, (b) the y-axis, and (c) the origin.
Plot the point (-2, 3). Then plot the point that is symmetric to it with respect to (a) the x-axis, (b) the y-axis, and (c) the origin.
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For the given equation, list the intercepts and test for symmetry: x² + y - 144 = 0. What is/are the intercept(s)?
For the given equation, list the intercepts and test for symmetry: x² + y - 144 = 0. What is/are the intercept(s)?
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For the given equation, list the intercepts and test for symmetry: x² + y - 144 = 0. Is the graph of the equation symmetric with respect to the x-axis?
For the given equation, list the intercepts and test for symmetry: x² + y - 144 = 0. Is the graph of the equation symmetric with respect to the x-axis?
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For the given equation, list the intercepts and test for symmetry: x² + y - 144 = 0. Is the graph of the equation symmetric with respect to the origin?
For the given equation, list the intercepts and test for symmetry: x² + y - 144 = 0. Is the graph of the equation symmetric with respect to the origin?
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For the given equation, list the intercepts and test for symmetry: y = x² - x - 42. What is/are the intercept(s)?
For the given equation, list the intercepts and test for symmetry: y = x² - x - 42. What is/are the intercept(s)?
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Flashcards
Solve 4 + 8n = 6n + 8
Solve 4 + 8n = 6n + 8
Find the value of 'n' that makes the equation true.
Solve 9x - (5x + 5) = 7x - 41
Solve 9x - (5x + 5) = 7x - 41
Find the value of 'x' that satisfies the equation.
Solve 3/7 * -x - 2 = -x
Solve 3/7 * -x - 2 = -x
Find the value of 'x' that satisfies the equation.
Solve 4x - 2 = 0
Solve 4x - 2 = 0
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Solve -6x + 8 ≤ 38
Solve -6x + 8 ≤ 38
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Solve -4(x + 2) < 16
Solve -4(x + 2) < 16
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Solve 0.5x - 15 ≤ 6
Solve 0.5x - 15 ≤ 6
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Pure acid needed for 70% mixture
Pure acid needed for 70% mixture
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Coffee mixture problem
Coffee mixture problem
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Candy mixture problem
Candy mixture problem
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Verify (3, 6) as solution
Verify (3, 6) as solution
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Verify (-2, -5) as a solution
Verify (-2, -5) as a solution
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Distance between (3,3) and (3,-5)
Distance between (3,3) and (3,-5)
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Midpoint of (-6,6) and (-9,-6)
Midpoint of (-6,6) and (-9,-6)
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Midpoint of (7,1) and (-16,-16)
Midpoint of (7,1) and (-16,-16)
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Is (8, 8) on x² - y² = 64?
Is (8, 8) on x² - y² = 64?
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y² = x + 1 intercepts/symmetry
y² = x + 1 intercepts/symmetry
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16x² + y² = 16 intercepts/symmetry
16x² + y² = 16 intercepts/symmetry
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Symmetry of x² + y - 1 = 0
Symmetry of x² + y - 1 = 0
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Symmetry of 16x² + y² = 16
Symmetry of 16x² + y² = 16
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Points on y² = x² + 256
Points on y² = x² + 256
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Points on x² + y² = 4
Points on x² + y² = 4
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Symmetry of (-2, 3)
Symmetry of (-2, 3)
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Symmetry of (6, -2)
Symmetry of (6, -2)
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x² + y - 144 = 0 intercepts/symmetry
x² + y - 144 = 0 intercepts/symmetry
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y = x²-x-42 intercepts/symmetry
y = x²-x-42 intercepts/symmetry
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Study Notes
Solving Equations and Inequalities
- Students are expected to solve basic algebraic equations and inequalities.
- The problems involve various operations including addition, subtraction, multiplication, and division.
- Students need to isolate the variable to find the solution.
Solving Inequalities
- To express the solution using set-builder notation, students identify the variable restrictions.
- To express the solution using interval notation, students use interval notation appropriate for the context.
- Graphing the solution set visually represents solutions.
Solving Equations
- Students are expected to solve systems of equations.
- Solving for variables is a key skill, isolated through various approaches.
Equations and Inequalities
- Solving for variables involves various steps, including simplification and combining like terms.
- Set notation and interval notation are used to express solutions for inequalities.
- Graphing demonstrates the solution set visually.
Systems of Equations
- Systems of equations are solved or verified for solutions.
- The solutions or verification of solutions are indicated by correct or incorrect.
Distance and Midpoint Formulas
- Students calculate distances between points using the distance formula.
- Students calculate midpoints of line segments using the midpoint formula.
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Description
This quiz focuses on solving basic algebraic equations and inequalities, including operations like addition, subtraction, multiplication, and division. Students will learn to express solutions using set-builder and interval notation, as well as graphing the solution sets. Key skills include isolating variables and working with systems of equations.
