Solve for x 7(x+7)=9(9+10)

$7 (x + 7) = 9 (9 + 10)$

Step 1

Simplify.

Add $9$ and $10$ .

$7 (x + 7) = 9 \cdot 19$

Multiply $9$ by $19$ .

$7 (x + 7) = 171$

Step 2

Divide each term in $7 (x + 7) = 171$ by $7$ and simplify.

Divide each term in $7 (x + 7) = 171$ by $7$ .

$\frac{7 (x + 7)}{7} = \frac{171}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (x + 7)}{7} = \frac{171}{7}$

Divide $x + 7$ by $1$ .

$x + 7 = \frac{171}{7}$

Step 3

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

Subtract $7$ from both sides of the equation.

$x = \frac{171}{7} - 7$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = \frac{171}{7} - 7 \cdot \frac{7}{7}$

Combine $- 7$ and $\frac{7}{7}$ .

$x = \frac{171}{7} + \frac{- 7 \cdot 7}{7}$

Combine the numerators over the common denominator.

$x = \frac{171 - 7 \cdot 7}{7}$

Simplify the numerator.

Multiply $- 7$ by $7$ .

$x = \frac{171 - 49}{7}$

Subtract $49$ from $171$ .

$x = \frac{122}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{122}{7}$

Decimal Form:

$x = 17.42857142 \dots$

Mixed Number Form:

$x = 17 \frac{3}{7}$