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

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

Step 1

Simplify $\frac{1}{2} - (\frac{5}{4} x + 8)$ .

Simplify each term.

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

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

Apply the distributive property.

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

Multiply $- 1$ by $8$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 8$ by $2$ .

$- \frac{5 x}{4} + \frac{1 - 16}{2} = - (- 2 x + 5) - 1$

Subtract $16$ from $1$ .

$- \frac{5 x}{4} + \frac{- 15}{2} = - (- 2 x + 5) - 1$

Move the negative in front of the fraction.

$- \frac{5 x}{4} - \frac{15}{2} = - (- 2 x + 5) - 1$

Step 2

Simplify $- (- 2 x + 5) - 1$ .

Simplify each term.

Apply the distributive property.

$- \frac{5 x}{4} - \frac{15}{2} = - (- 2 x) - 1 \cdot 5 - 1$

Multiply $- 2$ by $- 1$ .

$- \frac{5 x}{4} - \frac{15}{2} = 2 x - 1 \cdot 5 - 1$

Multiply $- 1$ by $5$ .

$- \frac{5 x}{4} - \frac{15}{2} = 2 x - 5 - 1$

Subtract $1$ from $- 5$ .

$- \frac{5 x}{4} - \frac{15}{2} = 2 x - 6$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$- \frac{5 x}{4} - \frac{15}{2} - 2 x = - 6$

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

$- \frac{5 x}{4} - 2 x \cdot \frac{4}{4} - \frac{15}{2} = - 6$

Combine $- 2 x$ and $\frac{4}{4}$ .

$- \frac{5 x}{4} + \frac{- 2 x \cdot 4}{4} - \frac{15}{2} = - 6$

Combine the numerators over the common denominator.

$\frac{- 5 x - 2 x \cdot 4}{4} - \frac{15}{2} = - 6$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 5 x - 2 x \cdot 4$ .

Factor $x$ out of $- 5 x$ .

$\frac{x \cdot - 5 - 2 x \cdot 4}{4} - \frac{15}{2} = - 6$

Factor $x$ out of $- 2 x \cdot 4$ .

$\frac{x \cdot - 5 + x (- 2 \cdot 4)}{4} - \frac{15}{2} = - 6$

Factor $x$ out of $x \cdot - 5 + x (- 2 \cdot 4)$ .

$\frac{x (- 5 - 2 \cdot 4)}{4} - \frac{15}{2} = - 6$

Multiply $- 2$ by $4$ .

$\frac{x (- 5 - 8)}{4} - \frac{15}{2} = - 6$

Subtract $8$ from $- 5$ .

$\frac{x \cdot - 13}{4} - \frac{15}{2} = - 6$

Move $- 13$ to the left of $x$ .

$\frac{- 13 \cdot x}{4} - \frac{15}{2} = - 6$

Move the negative in front of the fraction.

$- \frac{13 x}{4} - \frac{15}{2} = - 6$

Step 4

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

Add $\frac{15}{2}$ to both sides of the equation.

$- \frac{13 x}{4} = - 6 + \frac{15}{2}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{13 x}{4} = - 6 \cdot \frac{2}{2} + \frac{15}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$- \frac{13 x}{4} = \frac{- 6 \cdot 2}{2} + \frac{15}{2}$

Combine the numerators over the common denominator.

$- \frac{13 x}{4} = \frac{- 6 \cdot 2 + 15}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$- \frac{13 x}{4} = \frac{- 12 + 15}{2}$

Add $- 12$ and $15$ .

$- \frac{13 x}{4} = \frac{3}{2}$

Step 5

Multiply both sides of the equation by $- \frac{4}{13}$ .

$- \frac{4}{13} (- \frac{13 x}{4}) = - \frac{4}{13} \cdot \frac{3}{2}$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{13} (- \frac{13 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{13}$ into the numerator.

$\frac{- 4}{13} (- \frac{13 x}{4}) = - \frac{4}{13} \cdot \frac{3}{2}$

Move the leading negative in $- \frac{13 x}{4}$ into the numerator.

$\frac{- 4}{13} \cdot \frac{- 13 x}{4} = - \frac{4}{13} \cdot \frac{3}{2}$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{13} \cdot \frac{- 13 x}{4} = - \frac{4}{13} \cdot \frac{3}{2}$

Cancel the common factor.

$\frac{4 \cdot - 1}{13} \cdot \frac{- 13 x}{4} = - \frac{4}{13} \cdot \frac{3}{2}$

Rewrite the expression.

$\frac{- 1}{13} (- 13 x) = - \frac{4}{13} \cdot \frac{3}{2}$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 x$ .

$\frac{- 1}{13} (13 (- x)) = - \frac{4}{13} \cdot \frac{3}{2}$

Cancel the common factor.

$\frac{- 1}{13} (13 (- x)) = - \frac{4}{13} \cdot \frac{3}{2}$

Rewrite the expression.

$- - x = - \frac{4}{13} \cdot \frac{3}{2}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{13} \cdot \frac{3}{2}$

Multiply $x$ by $1$ .

$x = - \frac{4}{13} \cdot \frac{3}{2}$

Simplify the right side.

Simplify $- \frac{4}{13} \cdot \frac{3}{2}$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{4}{13}$ into the numerator.

$x = \frac{- 4}{13} \cdot \frac{3}{2}$

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{- 2}{13}$ and $3$ .

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

Simplify the expression.

Multiply $- 2$ by $3$ .

$x = \frac{- 6}{13}$

Move the negative in front of the fraction.

$x = - \frac{6}{13}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{6}{13}$

Decimal Form:

$x = - 0.\overline{461538}$

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

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