Solve for x 6<(12+x)/3<10

$6 < \frac{12 + x}{3} < 10$

Step 1

Multiply each term in the inequality by $3$ .

$6 \cdot 3 < \frac{12 + x}{3} \cdot 3 < 10 \cdot 3$

Step 2

Multiply $6$ by $3$ .

$18 < \frac{12 + x}{3} \cdot 3 < 10 \cdot 3$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$18 < \frac{12 + x}{3} \cdot 3 < 10 \cdot 3$

Rewrite the expression.

$18 < 12 + x < 10 \cdot 3$

Step 4

Multiply $10$ by $3$ .

$18 < 12 + x < 30$

Step 5

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

Subtract $12$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$18 - 12 < x < 30 - 12$

Subtract $12$ from $18$ .

$6 < x < 30 - 12$

Subtract $12$ from $30$ .

$6 < x < 18$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$6 < x < 18$

Interval Notation:

$(6, 18)$

Step 7