Solve for x 3=-2(-5/4x+7/8)+x

$3 = - 2 (- \frac{5}{4} x + \frac{7}{8}) + x$

Step 1

Rewrite the equation as $- 2 (- \frac{5}{4} x + \frac{7}{8}) + x = 3$ .

$- 2 (- \frac{5}{4} x + \frac{7}{8}) + x = 3$

Step 2

Simplify $- 2 (- \frac{5}{4} x + \frac{7}{8}) + x$ .

Simplify each term.

Combine $x$ and $\frac{5}{4}$ .

$- 2 (- \frac{x \cdot 5}{4} + \frac{7}{8}) + x = 3$

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

$- 2 (- \frac{5 x}{4} + \frac{7}{8}) + x = 3$

Apply the distributive property.

$- 2 (- \frac{5 x}{4}) - 2 (\frac{7}{8}) + x = 3$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 x}{4}$ into the numerator.

$- 2 \frac{- 5 x}{4} - 2 (\frac{7}{8}) + x = 3$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- 5 x}{4} - 2 (\frac{7}{8}) + x = 3$

Factor $2$ out of $4$ .

$2 \cdot - 1 \frac{- 5 x}{2 \cdot 2} - 2 (\frac{7}{8}) + x = 3$

Cancel the common factor.

$2 \cdot - 1 \frac{- 5 x}{2 \cdot 2} - 2 (\frac{7}{8}) + x = 3$

Rewrite the expression.

$- 1 \frac{- 5 x}{2} - 2 (\frac{7}{8}) + x = 3$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$- 1 \frac{- 5 x}{2} + 2 (- 1) \frac{7}{8} + x = 3$

Factor $2$ out of $8$ .

$- 1 \frac{- 5 x}{2} + 2 \cdot - 1 \frac{7}{2 \cdot 4} + x = 3$

Cancel the common factor.

$- 1 \frac{- 5 x}{2} + 2 \cdot - 1 \frac{7}{2 \cdot 4} + x = 3$

Rewrite the expression.

$- 1 \frac{- 5 x}{2} - 1 (\frac{7}{4}) + x = 3$

Simplify each term.

Move the negative in front of the fraction.

$- 1 (- \frac{(5) x}{2}) - 1 (\frac{7}{4}) + x = 3$

Multiply $- 1 (- \frac{5 x}{2})$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{5 x}{2} - 1 (\frac{7}{4}) + x = 3$

Multiply $\frac{5 x}{2}$ by $1$ .

$\frac{5 x}{2} - 1 (\frac{7}{4}) + x = 3$

Rewrite $- 1 (\frac{7}{4})$ as $- (\frac{7}{4})$ .

$\frac{5 x}{2} - \frac{7}{4} + x = 3$

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

$\frac{5 x}{2} + x \cdot \frac{2}{2} - \frac{7}{4} = 3$

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

$\frac{5 x}{2} + \frac{x \cdot 2}{2} - \frac{7}{4} = 3$

Combine the numerators over the common denominator.

$\frac{5 x + x \cdot 2}{2} - \frac{7}{4} = 3$

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

Reorder $x$ and $2$ .

$\frac{5 x + 2 \cdot x}{2} - \frac{7}{4} = 3$

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

$\frac{7 x}{2} - \frac{7}{4} = 3$

Step 3

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

Add $\frac{7}{4}$ to both sides of the equation.

$\frac{7 x}{2} = 3 + \frac{7}{4}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 x}{2} = 3 \cdot \frac{4}{4} + \frac{7}{4}$

Combine $3$ and $\frac{4}{4}$ .

$\frac{7 x}{2} = \frac{3 \cdot 4}{4} + \frac{7}{4}$

Combine the numerators over the common denominator.

$\frac{7 x}{2} = \frac{3 \cdot 4 + 7}{4}$

Simplify the numerator.

Multiply $3$ by $4$ .

$\frac{7 x}{2} = \frac{12 + 7}{4}$

Add $12$ and $7$ .

$\frac{7 x}{2} = \frac{19}{4}$

Step 4

Multiply both sides of the equation by $\frac{2}{7}$ .

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot \frac{19}{4}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{7} \cdot \frac{7 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot \frac{19}{4}$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot \frac{19}{4}$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{2}{7} \cdot \frac{19}{4}$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot \frac{19}{4}$

Rewrite the expression.

$x = \frac{2}{7} \cdot \frac{19}{4}$

Simplify the right side.

Simplify $\frac{2}{7} \cdot \frac{19}{4}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{2}{7} \cdot \frac{19}{2 (2)}$

Cancel the common factor.

$x = \frac{2}{7} \cdot \frac{19}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{7} \cdot \frac{19}{2}$

Multiply $\frac{1}{7}$ by $\frac{19}{2}$ .

$x = \frac{19}{7 \cdot 2}$

Multiply $7$ by $2$ .

$x = \frac{19}{14}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{14}$

Decimal Form:

$x = 1.35714285 \dots$

Mixed Number Form:

$x = 1 \frac{5}{14}$

Solve for x 3=-2(-5/4x+7/8)+x

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