Solve for x 18<4x+2<24

$18 < 4 x + 2 < 24$

Step 1

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$18 - 2 < 4 x < 24 - 2$

Subtract $2$ from $18$ .

$16 < 4 x < 24 - 2$

Subtract $2$ from $24$ .

$16 < 4 x < 22$

Step 2

Divide each term in the inequality by $4$ .

$\frac{16}{4} < \frac{4 x}{4} < \frac{22}{4}$

Step 3

Divide $16$ by $4$ .

$4 < \frac{4 x}{4} < \frac{22}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$4 < \frac{4 x}{4} < \frac{22}{4}$

Divide $x$ by $1$ .

$4 < x < \frac{22}{4}$

Step 5

Cancel the common factor of $22$ and $4$ .

Factor $2$ out of $22$ .

$4 < x < \frac{2 (11)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$4 < x < \frac{2 \cdot 11}{2 \cdot 2}$

Cancel the common factor.

$4 < x < \frac{2 \cdot 11}{2 \cdot 2}$

Rewrite the expression.

$4 < x < \frac{11}{2}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$4 < x < \frac{11}{2}$

Interval Notation:

$(4, \frac{11}{2})$

Step 7