Solve for x -7<5x+3<18

$- 7 < 5 x + 3 < 18$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 7 - 3 < 5 x < 18 - 3$

Subtract $3$ from $- 7$ .

$- 10 < 5 x < 18 - 3$

Subtract $3$ from $18$ .

$- 10 < 5 x < 15$

Step 2

Divide each term in the inequality by $5$ .

$\frac{- 10}{5} < \frac{5 x}{5} < \frac{15}{5}$

Step 3

Divide $- 10$ by $5$ .

$- 2 < \frac{5 x}{5} < \frac{15}{5}$

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

$- 2 < \frac{5 x}{5} < \frac{15}{5}$

Divide $x$ by $1$ .

$- 2 < x < \frac{15}{5}$

Step 5

Divide $15$ by $5$ .

$- 2 < x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x < 3$

Interval Notation:

$(- 2, 3)$

Step 7