Algebraic Equations and Inequalities
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Questions and Answers

Solve the equation: 4 + 8n = 6n + 8

n = 2

Solve the equation: 9x - (5x + 5) = 7x - 41

x = -18

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}.

<p>≥</p> Signup and view all the answers

Solve the inequality: -6x + 8 ≤ 38. Express the solution using interval notation. The solution set is [blank]

<p>[-5,∞]</p> Signup and view all the answers

Solve the inequality: -4(x + 2) < 16. Express the solution using set notation. The solution is expressed in set notation as {x | x ______ -6}.

<blockquote> </blockquote> Signup and view all the answers

Solve the inequality: -4(x + 2) < 16. Express the solution using interval notation. The solution is expressed in interval notation as [blank]

<p>(-∞,-6)</p> Signup and view all the answers

Solve the inequality: 0.5x - 15 ≤ 6. Express the solution using set notation. The solution is expressed in set notation as {x | x ______ 22}.

<p>≤</p> Signup and view all the answers

Solve the inequality: 0.5x - 15 ≤ 6. Express the solution using interval notation. The solution is expressed in interval notation as [blank]

<p>(∞,22]</p> Signup and view all the answers

How much pure acid should be mixed with 6 gallons of a 60% acid solution to get a 70% acid solution?

<p>2 gallons</p> Signup and view all the answers

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?

<p>45 pounds</p> Signup and view all the answers

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?

<p>20 pounds</p> Signup and view all the answers

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

<p>True</p> Signup and view all the answers

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

<p>True</p> Signup and view all the answers

Find the distance d(P1,P2) between the points P1 and P2: P1 = (3,3); P2 = (3, -5)

<p>8</p> Signup and view all the answers

Find the midpoint of the line segment joining the points P1 and P2: P1 = (-6,6); P2 = (-9, -6)

<p>(-15/2, 0)</p> Signup and view all the answers

Find the midpoint of the line segment joining the points P1 and P2: P1 = (7,1) ; P2 = (-16, -16)

<p>(-9/2, -15/2)</p> Signup and view all the answers

Determine whether the point (8,8) is on the graph of the equation: x² - y² = 64

<p>False</p> Signup and view all the answers

List the intercepts and type(s) of symmetry, if any: y² = x + 1

<p>intercepts: (-1,0), (0,1), (0,-1); symmetric with respect to x-axis</p> Signup and view all the answers

List the intercepts and type(s) of symmetry, if any: 16x² + y² = 16

<p>intercepts: (1,0), (-1,0), (0,4), (0,-4); symmetric with respect to x-axis, y-axis, and origin</p> Signup and view all the answers

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

<p>x-axis</p> Signup and view all the answers

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

<p>x-axis, y-axis, origin</p> Signup and view all the answers

Determine whether the given points are on the graph of the equation: y² = x² + 256. Points (0,16), (16,0), (-16, 0)

<p>(-16,0)</p> Signup and view all the answers

Determine which of the given points are on the graph of the equation: x² + y² = 4. Points: (2,0), (-2,2), (√2, √2)

<p>(2,0)</p> Signup and view all the answers

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.

<p>(a) Plot the point that is symmetric to (-2,3) with respect to the x-axis. = (-2, -3) (b) Plot the point that is symmetric to (-2,3) with respect to the y-axis. = (2, 3) (c) Plot the point that is symmetric to (-2,3) with respect to the origin. = (2, -3)</p> Signup and view all the answers

For the given equation, list the intercepts and test for symmetry: x² + y - 144 = 0. What is/are the intercept(s)?

<p>The intercept(s) is/are [blank] (Type an ordered pair. Use a comma to separate answers as needed.)</p> Signup and view all the answers

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?

<p>False</p> Signup and view all the answers

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?

<p>False</p> Signup and view all the answers

For the given equation, list the intercepts and test for symmetry: y = x² - x - 42. What is/are the intercept(s)?

<p>The intercept(s) is/are [blank] (Type an ordered pair. Use a comma to separate answers as needed.)</p> Signup and view all the answers

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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Final Exam Review PDF AQA 2024

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.

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