Podcast Beta
Questions and Answers
What is the solution to the inequality $-2x \geq 4$?
What is the largest prime number value of $x$ that satisfies the inequality $8 - x > 3$?
What is the smallest rational value of $x$ that satisfies the inequality $3x \leq 8x - 5$?
For the inequality $5(x + 3) \geq 9$, what is the solution for $x$?
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What is the smallest possible value of $x$ that is a perfect square and satisfies $-4y - 5 \geq 11$?
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In the equation $2x + y = 2$, when $x = -4$, the value of $y$ is _____
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In the equation $2x + y = 2$, when $x = 0$, the value of $y$ is _____
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In the equation $2x + y = 2$, when $x = 4$, the value of $y$ is _____
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What is the value of p if the point (p, -2) lies on the graph of $2x + y = 2$?
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The coordinates of the point of intersection of the graphs of $2x + y = 2$ and $x = -0.5$ are _____
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Find the value of p when $5x - 3y = 2$ and $x = -5$.
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If $5x - 3y = 2$ and $x = -2$, what is the value of y?
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Find the value of q when $5x - 3y = 2$ and $x = 7$.
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What are the simultaneous equations to solve when $5x - 3y = 2$ and $3x + 4y = 7$?
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What is the first number if 11 is added to it, resulting in a number twice the second number?
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What is the difference in price between 1 cup of ice-cream milk tea and 1 cup of bubble tea if 5 cups and 4 cups costs $26.80 and 7 cups and 6 cups costs $38.60?
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Study Notes
Solving Inequalities
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Solve the inequality -2x ≥ 4
- Divide both sides of the inequality by -2, remembering to flip the inequality sign
- The solution is x ≤ -2.
- Represent this solution on a number line with a closed circle at -2 and a line extending to the left.
-
Solve the inequality x + 4 < 3
- Subtract 4 from both sides of the inequality.
- The solution is x < -1.
- Represent this solution on a number line with an open circle at -1 and a line extending to the left.
-
Solve the inequality -4y - 5 ≥ 11
- Add 5 to both sides of the inequality.
- Divide both sides of the inequality by -4, remembering to flip the inequality sign.
- The solution is y ≤ -4.
- Represent this solution on a number line with a closed circle at -4 and a line extending to the left.
-
Solve the inequality -2y + 4 > 3
- Subtract 4 from both sides of the inequality.
- Divide both sides of the inequality by -2, remembering to flip the inequality sign.
- The solution is y < 1/2.
- Represent this solution on a number line with an open circle at 1/2 and a line extending to the left.
-
Solve the inequality x - 3 ≥ 7
- Add 3 to both sides of the inequality.
- The solution is x ≥ 10.
- Represent this solution on a number line with a closed circle at 10 and a line extending to the right.
Solving Inequalities with Conditions
-
Solve the inequality 8 - x > 3.
- Subtract 8 from both sides of the inequality.
- Multiply both sides of the inequality by -1, remembering to flip the inequality sign.
- The solution is x < 5.
- Represent this solution on a number line with an open circle at 5 and a line extending to the left.
-
Find the largest possible value of x that satisfies the inequality 8 - x > 3 if x is a prime number
- The largest prime number less than 5 is 3
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Find the positive integer value of x that satisfies the inequality 8 - x > 3.
- The positive integer that satisfies the inequality is 4.
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Find the largest possible value of x that satisfies the inequality 8 - x > 3 if x is a perfect square.
- The largest perfect square that satisfies the inequality is 4.
Additional Inequality Problems
-
Solve the inequality 3x ≤ 8x - 5.
- Subtract 3x from both sides of the inequality.
- Divide both sides by 5.
- The solution is x ≥ 1.
- Represent this solution on a number line with a closed circle at 1 and a line extending to the right.
-
Find the smallest possible value of x that satisfies the inequality 3x ≤ 8x - 5 if x is a prime number.
- The smallest prime number that satisfies the inequality is 2.
-
Find the smallest rational value of x that satisfies the inequality 3x ≤ 8x - 5.
- The smallest rational value that satisfies the inequality is 1.
-
Find the smallest perfect cube that satisfies the inequality 3x ≤ 8x - 5.
- The smallest perfect cube that satisfies the inequality is 1.
Solving More Complex Inequalities
-
Solve the inequality 5(x + 3) ≥ 9.
- Distribute the 5 on the left side of the inequality.
- Subtract 15 from both sides.
- Divide both sides by 5.
- The solution is x ≥ -6/5.
- Represent this solution on a number line with a closed circle at -6/5 and a line extending to the right.
-
Solve the inequality 𝑦+1/3 > 1/2.
- Subtract 1/3 from both sides of the inequality.
- The solution is y > 1/6.
- Represent this solution on a number line with an open circle at 1/6 and a line extending to the right.
Linear Equations
-
Solve for
yin the equation2x + y = 2to create a table of values forxandy -
Graphing Linear Equations
-
Draw the graph of
2x + y = 2for-4 ≤ x ≤ 4on a sheet of graph paper using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis -
Identify the point (p, -2) on the graph and find the value of
p -
Draw the graph of
x = -0.5on the same axes -
Find the coordinates of the point where the graphs of
2x + y = 2andx = -0.5intersect -
Solving Systems of Equations
-
Find the values of
pandqin the equation5x - 3y = 2using the table of values provided -
Graph the equation
5x - 3y = 2for-5 ≤ x ≤ 7on a sheet of graph paper using a scale of 1 cm to represent 1 unit on both axes -
Create a table of values for
xandyin the equation3x + 4y = 7 -
Graph the equation
3x + 4y = 7on the same axes as the previous graph -
Find the solution to the system of equations
5x - 3y = 2and3x + 4y = 7by identifying the point of intersection on the graph -
Simultaneous Equations
-
Solve the simultaneous equations
7x + 2y = 10and5x - 4y = 28 -
Solve the simultaneous equations
5x + 2y = 6and2x - y = 2.5 -
Word Problems
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Let the first number be
xand the second number bey -
Formulate two equations based on the given information: -
x + 11 = 2y-y + 20 = 2x -
Solve the simultaneous equations to find the two numbers
-
Real-World Problems
-
Let the cost of 1 cup of ice-cream milk tea be
xand the cost of 1 cup of bubble tea bey -
Formulate two equations based on the given information: -
5x + 4y = 26.80-7x + 6y = 38.60 -
Solve the simultaneous equations to find the difference between
xandy
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Description
This quiz focuses on solving inequalities and representing solutions on number lines. It includes various types of inequalities, demonstrating the process of isolating the variable and graphing the results. Test your knowledge and skills in algebraic problem-solving.
