Solve the System of @WORD -7<5x+3<18

$- 7 < 5 x + 3 < 18$

Step 1

Solve $- 7 < 5 x + 3$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$5 x + 3 > - 7$

Move all terms not containing $x$ to the right side of the inequality.

Subtract $3$ from both sides of the inequality.

$5 x > - 7 - 3$

Subtract $3$ from $- 7$ .

$5 x > - 10$

Divide each term in $5 x > - 10$ by $5$ and simplify.

Divide each term in $5 x > - 10$ by $5$ .

$\frac{5 x}{5} > \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} > \frac{- 10}{5}$

Divide $x$ by $1$ .

$x > \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$x > - 2$

Step 2

Solve $5 x + 3 < 18$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Subtract $3$ from both sides of the inequality.

$5 x < 18 - 3$

Subtract $3$ from $18$ .

$5 x < 15$

Divide each term in $5 x < 15$ by $5$ and simplify.

Divide each term in $5 x < 15$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $15$ by $5$ .

$x < 3$

Step 3

Find the intersection of $x > - 2$ and $x < 3$ .

$- 2 < x < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x < 3$

Interval Notation:

$(- 2, 3)$

Step 5

Solve the System of @WORD -7<5x+3<18

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