Solve for x (5(x-3))/8+2=7

$\frac{5 (x - 3)}{8} + 2 = 7$

Step 1

Simplify $\frac{5 (x - 3)}{8} + 2$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5 (x - 3)}{8} + 2 \cdot \frac{8}{8} = 7$

Simplify terms.

Combine $2$ and $\frac{8}{8}$ .

$\frac{5 (x - 3)}{8} + \frac{2 \cdot 8}{8} = 7$

Combine the numerators over the common denominator.

$\frac{5 (x - 3) + 2 \cdot 8}{8} = 7$

Simplify the numerator.

Apply the distributive property.

$\frac{5 x + 5 \cdot - 3 + 2 \cdot 8}{8} = 7$

Multiply $5$ by $- 3$ .

$\frac{5 x - 15 + 2 \cdot 8}{8} = 7$

Multiply $2$ by $8$ .

$\frac{5 x - 15 + 16}{8} = 7$

Add $- 15$ and $16$ .

$\frac{5 x + 1}{8} = 7$

Step 2

Multiply both sides by $8$ .

$\frac{5 x + 1}{8} \cdot 8 = 7 \cdot 8$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{5 x + 1}{8} \cdot 8 = 7 \cdot 8$

Rewrite the expression.

$5 x + 1 = 7 \cdot 8$

Simplify the right side.

Multiply $7$ by $8$ .

$5 x + 1 = 56$

Step 4

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$5 x = 56 - 1$

Subtract $1$ from $56$ .

$5 x = 55$

Divide each term in $5 x = 55$ by $5$ and simplify.

Divide each term in $5 x = 55$ by $5$ .

$\frac{5 x}{5} = \frac{55}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{55}{5}$

Divide $x$ by $1$ .

$x = \frac{55}{5}$

Simplify the right side.

Divide $55$ by $5$ .

$x = 11$

Solve for x (5(x-3))/8+2=7

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