Solve for x 5(5x+9)=13-(x+7)

$5 (5 x + 9) = 13 - (x + 7)$

Step 1

Simplify $5 (5 x + 9)$ .

Rewrite.

$0 + 0 + 5 (5 x + 9) = 13 - (x + 7)$

Simplify by adding zeros.

$5 (5 x + 9) = 13 - (x + 7)$

Apply the distributive property.

$5 (5 x) + 5 \cdot 9 = 13 - (x + 7)$

Multiply.

Multiply $5$ by $5$ .

$25 x + 5 \cdot 9 = 13 - (x + 7)$

Multiply $5$ by $9$ .

$25 x + 45 = 13 - (x + 7)$

Step 2

Simplify $13 - (x + 7)$ .

Simplify each term.

Apply the distributive property.

$25 x + 45 = 13 - x - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$25 x + 45 = 13 - x - 7$

Subtract $7$ from $13$ .

$25 x + 45 = - x + 6$

Step 3

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$25 x + 45 + x = 6$

Add $25 x$ and $x$ .

$26 x + 45 = 6$

Step 4

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

Subtract $45$ from both sides of the equation.

$26 x = 6 - 45$

Subtract $45$ from $6$ .

$26 x = - 39$

Step 5

Divide each term in $26 x = - 39$ by $26$ and simplify.

Divide each term in $26 x = - 39$ by $26$ .

$\frac{26 x}{26} = \frac{- 39}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} = \frac{- 39}{26}$

Divide $x$ by $1$ .

$x = \frac{- 39}{26}$

Simplify the right side.

Cancel the common factor of $- 39$ and $26$ .

Factor $13$ out of $- 39$ .

$x = \frac{13 (- 3)}{26}$

Cancel the common factors.

Factor $13$ out of $26$ .

$x = \frac{13 \cdot - 3}{13 \cdot 2}$

Cancel the common factor.

$x = \frac{13 \cdot - 3}{13 \cdot 2}$

Rewrite the expression.

$x = \frac{- 3}{2}$

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{2}$

Decimal Form:

$x = - 1.5$

Mixed Number Form:

$x = - 1 \frac{1}{2}$

Solve for x 5(5x+9)=13-(x+7)

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