### Home > INT1 > Chapter 10 > Lesson 10.2.3 > Problem10-108

10-108.

Solve each inequality below. Represent the solutions on number lines.

1. $7x - 2 < 3 + 2x$

Find the boundary point.
$7x − 2 = 3 + 2x$

Solve for $x$.
$5x = 5$
$x = 1$

Test numbers on both sides of 1.

$7\left(0\right) − 2 \lt 3 + 2\left(0\right)$
$0 − 2 \lt 3 + 0$
$−2 \lt 3$
True

$7\left(2\right) − 2 \lt 3 + 2\left(2\right)$$14 − 2 \lt 3 + 4$
$12 \lt 7$
False

$x \lt 1$

1. $\frac{1}{3}x\ge2$

Follow the steps in part (a).

1. $3(2m-1)-5m\le-1$

Follow the steps in part (a).

1. $2k+3\le2k+1$

Follow the steps in part (a).

Does this inequality have a solution?

Use the eTool below to represent the solutions on number lines.
Click the link at right for the full version of the eTool: Int1 10-108 HW eTool