Lesson 20: Practice Problems

Problem 1

Here is a graph of the equation $2 y - x = 1$ .

A coordinate grid with a positive slope line.

Are the points $(0, \frac{1}{2})$ and $(- 7, - 3)$ solutions to the equation? Explain or show how you know.
Check if each of these points is a solution to the inequality $2 y - x > 1$ :
- $(0, 2)$
- $(8, \frac{1}{2})$
- $(- 6, 3)$
- $(- 7, - 3)$
Shade the region that represents the solution set to the inequality $2 y - x > 1$ .
Are the points on the line included in the solution set? Explain how you know.

Problem 2

Select all coordinate pairs that are solutions to the inequality $5 x + 9 y < 45$ .

$(0, 0)$
$(5, 0)$
$(9, 0)$
$(0, 5)$
$(0, 9)$
$(5, 9)$
$(- 5, - 9)$

Problem 3

Consider the linear equation $2 y - 3 x = 5$ .

The pair $(- 1, 1)$ is a solution to the equation. Find another $(x, y)$ pair that is a solution to the equation.
Are $(- 1, 1)$ and $(4, 1)$ solutions to the inequality $2 y - 3 x < 5$ ? Explain how you know.
Explain how to use the answers to the previous questions to graph the solution set to the inequality $2 y - 3 x < 5$ .

Problem 4

The boundary line on the graph represents the equation $5 x + 2 y = 6$ . Write an inequality that is represented by the graph.

A coordinate grid with a dotted line intersecting the y axis at (0,3) and blue shading to the left.

Problem 5

Choose the inequality whose solution set is represented by this graph.

A coordinate grid with a dotted positive slope line and blue shading above it.

$x - 3 y < 5$
$x - 3 y \leq 5$
$x - 3 y > 5$
$x - 3 y \geq 5$

Problem 6

Elena is planning to go camping for the weekend and has already spent $40 on supplies. She goes to the store and buys more supplies.

Which inequality represents $d$ , the total amount in dollars that Elena spends on supplies?

$d > 40$
$d \geq 40$
$d < 40$
$d \leq 40$

Problem 7

Solve this inequality: $\frac{x - 4}{3} \geq \frac{x + 3}{2}$

Problem 8

Which graph represents the solution to $\frac{4 x - 8}{3} \leq 2 x - 5$ ?

Problem 9

Solve $- x < 3$ . Explain how to find the solution set.