Solve for x 1/4x+2=-5/8x-5

$\frac{1}{4} x + 2 = - \frac{5}{8} x - 5$

Step 1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + 2 = - \frac{5}{8} x - 5$

Step 2

Simplify each term.

Combine $x$ and $\frac{5}{8}$ .

$\frac{x}{4} + 2 = - \frac{x \cdot 5}{8} - 5$

Move $5$ to the left of $x$ .

$\frac{x}{4} + 2 = - \frac{5 x}{8} - 5$

Step 3

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

Add $\frac{5 x}{8}$ to both sides of the equation.

$\frac{x}{4} + 2 + \frac{5 x}{8} = - 5$

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} \cdot \frac{2}{2} + \frac{5 x}{8} + 2 = - 5$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{4}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{4 \cdot 2} + \frac{5 x}{8} + 2 = - 5$

Multiply $4$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $x \cdot 2$ and $5 x$ .

Reorder $x$ and $2$ .

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

Add $2 \cdot x$ and $5 x$ .

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

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

Step 4

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

Subtract $2$ from both sides of the equation.

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

Subtract $2$ from $- 5$ .

$\frac{7 x}{8} = - 7$

Step 5

Multiply both sides of the equation by $\frac{8}{7}$ .

$\frac{8}{7} \cdot \frac{7 x}{8} = \frac{8}{7} \cdot - 7$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{8}{7} \cdot \frac{7 x}{8}$ .

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{7} \cdot \frac{7 x}{8} = \frac{8}{7} \cdot - 7$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{8}{7} \cdot - 7$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{8}{7} \cdot - 7$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{8}{7} \cdot - 7$

Rewrite the expression.

$x = \frac{8}{7} \cdot - 7$

Simplify the right side.

Simplify $\frac{8}{7} \cdot - 7$ .

Cancel the common factor of $7$ .

Factor $7$ out of $- 7$ .

$x = \frac{8}{7} \cdot (7 (- 1))$

Cancel the common factor.

$x = \frac{8}{7} \cdot (7 \cdot - 1)$

Rewrite the expression.

$x = 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$x = - 8$

Solve for x 1/4x+2=-5/8x-5

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