Solve for x -6/5*(4-x)=-4(x+1/2)

$- \frac{6}{5} \cdot (4 - x) = - 4 (x + \frac{1}{2})$

Step 1

Simplify $- \frac{6}{5} \cdot (4 - x)$ .

Rewrite.

$0 + 0 - \frac{6}{5} \cdot (4 - x) = - 4 (x + \frac{1}{2})$

Simplify by adding zeros.

$- \frac{6}{5} \cdot (4 - x) = - 4 (x + \frac{1}{2})$

Apply the distributive property.

$- \frac{6}{5} \cdot 4 - \frac{6}{5} (- x) = - 4 (x + \frac{1}{2})$

Multiply $- \frac{6}{5} \cdot 4$ .

Multiply $4$ by $- 1$ .

$- 4 (\frac{6}{5}) - \frac{6}{5} (- x) = - 4 (x + \frac{1}{2})$

Combine $- 4$ and $\frac{6}{5}$ .

$\frac{- 4 \cdot 6}{5} - \frac{6}{5} (- x) = - 4 (x + \frac{1}{2})$

Multiply $- 4$ by $6$ .

$\frac{- 24}{5} - \frac{6}{5} (- x) = - 4 (x + \frac{1}{2})$

Multiply $- \frac{6}{5} (- x)$ .

Multiply $- 1$ by $- 1$ .

$\frac{- 24}{5} + 1 (\frac{6}{5}) x = - 4 (x + \frac{1}{2})$

Multiply $\frac{6}{5}$ by $1$ .

$\frac{- 24}{5} + \frac{6}{5} x = - 4 (x + \frac{1}{2})$

Combine $\frac{6}{5}$ and $x$ .

$\frac{- 24}{5} + \frac{6 x}{5} = - 4 (x + \frac{1}{2})$

Move the negative in front of the fraction.

$- \frac{24}{5} + \frac{6 x}{5} = - 4 (x + \frac{1}{2})$

Step 2

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

Apply the distributive property.

$- \frac{24}{5} + \frac{6 x}{5} = - 4 x - 4 (\frac{1}{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$- \frac{24}{5} + \frac{6 x}{5} = - 4 x + 2 (- 2) \frac{1}{2}$

Cancel the common factor.

$- \frac{24}{5} + \frac{6 x}{5} = - 4 x + 2 \cdot - 2 \frac{1}{2}$

Rewrite the expression.

$- \frac{24}{5} + \frac{6 x}{5} = - 4 x - 2$

Step 3

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

Add $4 x$ to both sides of the equation.

$- \frac{24}{5} + \frac{6 x}{5} + 4 x = - 2$

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{24}{5} + \frac{6 x}{5} + 4 x \cdot \frac{5}{5} = - 2$

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

$- \frac{24}{5} + \frac{6 x}{5} + \frac{4 x \cdot 5}{5} = - 2$

Combine the numerators over the common denominator.

$- \frac{24}{5} + \frac{6 x + 4 x \cdot 5}{5} = - 2$

Combine the numerators over the common denominator.

$\frac{- 24 + 6 x + 4 x \cdot 5}{5} = - 2$

Multiply $5$ by $4$ .

$\frac{- 24 + 6 x + 20 x}{5} = - 2$

Add $6 x$ and $20 x$ .

$\frac{- 24 + 26 x}{5} = - 2$

Factor $2$ out of $- 24 + 26 x$ .

Factor $2$ out of $- 24$ .

$\frac{2 (- 12) + 26 x}{5} = - 2$

Factor $2$ out of $26 x$ .

$\frac{2 (- 12) + 2 (13 x)}{5} = - 2$

Factor $2$ out of $2 (- 12) + 2 (13 x)$ .

$\frac{2 (- 12 + 13 x)}{5} = - 2$

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{2 (- 1 (12) + 13 x)}{5} = - 2$

Factor $- 1$ out of $13 x$ .

$\frac{2 (- 1 (12) - (- 13 x))}{5} = - 2$

Factor $- 1$ out of $- 1 (12) - (- 13 x)$ .

$\frac{2 (- 1 (12 - 13 x))}{5} = - 2$

Move the negative in front of the fraction.

$- \frac{2 (12 - 13 x)}{5} = - 2$

Step 4

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2 (12 - 13 x)}{5}) = - \frac{5}{2} \cdot - 2$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{2} (- \frac{2 (12 - 13 x)}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 (12 - 13 x)}{5}) = - \frac{5}{2} \cdot - 2$

Move the leading negative in $- \frac{2 (12 - 13 x)}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 (12 - 13 x)}{5} = - \frac{5}{2} \cdot - 2$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 (12 - 13 x)}{5} = - \frac{5}{2} \cdot - 2$

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 (12 - 13 x)}{5} = - \frac{5}{2} \cdot - 2$

Rewrite the expression.

$\frac{- 1}{2} (- 2 (12 - 13 x)) = - \frac{5}{2} \cdot - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 (12 - 13 x)$ .

$\frac{- 1}{2} (2 (- (12 - 13 x))) = - \frac{5}{2} \cdot - 2$

Cancel the common factor.

$\frac{- 1}{2} (2 (- (12 - 13 x))) = - \frac{5}{2} \cdot - 2$

Rewrite the expression.

$- - (12 - 13 x) = - \frac{5}{2} \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (12 - 13 x) = - \frac{5}{2} \cdot - 2$

Multiply $12 - 13 x$ by $1$ .

$12 - 13 x = - \frac{5}{2} \cdot - 2$

Simplify the right side.

Simplify $- \frac{5}{2} \cdot - 2$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$12 - 13 x = \frac{- 5}{2} \cdot - 2$

Factor $2$ out of $- 2$ .

$12 - 13 x = \frac{- 5}{2} \cdot (2 (- 1))$

Cancel the common factor.

$12 - 13 x = \frac{- 5}{2} \cdot (2 \cdot - 1)$

Rewrite the expression.

$12 - 13 x = - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$12 - 13 x = 5$

Step 6

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

Subtract $12$ from both sides of the equation.

$- 13 x = 5 - 12$

Subtract $12$ from $5$ .

$- 13 x = - 7$

Step 7

Divide each term in $- 13 x = - 7$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 7$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 7}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 7}{- 13}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 13}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{7}{13}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{13}$

Decimal Form:

$x = 0.\overline{538461}$

Solve for x -6/5*(4-x)=-4(x+1/2)

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