Solve for x 5/4x=-(-5x-6)+3/2x

$\frac{5}{4} x = - (- 5 x - 6) + \frac{3}{2} x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- (- 5 x - 6) + \frac{3}{2} x = \frac{5}{4} x$

Step 2

Simplify $- (- 5 x - 6) + \frac{3}{2} x$ .

Simplify each term.

Apply the distributive property.

$- (- 5 x) - - 6 + \frac{3}{2} x = \frac{5}{4} x$

Multiply $- 5$ by $- 1$ .

$5 x - - 6 + \frac{3}{2} x = \frac{5}{4} x$

Multiply $- 1$ by $- 6$ .

$5 x + 6 + \frac{3}{2} x = \frac{5}{4} x$

Combine $\frac{3}{2}$ and $x$ .

$5 x + 6 + \frac{3 x}{2} = \frac{5}{4} x$

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x \cdot \frac{2}{2} + \frac{3 x}{2} + 6 = \frac{5}{4} x$

Simplify terms.

Combine $5 x$ and $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{2} + \frac{3 x}{2} + 6 = \frac{5}{4} x$

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 + 3 x}{2} + 6 = \frac{5}{4} x$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x \cdot 2 + 3 x$ .

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

$\frac{x (5 \cdot 2) + 3 x}{2} + 6 = \frac{5}{4} x$

Factor $x$ out of $3 x$ .

$\frac{x (5 \cdot 2) + x \cdot 3}{2} + 6 = \frac{5}{4} x$

Factor $x$ out of $x (5 \cdot 2) + x \cdot 3$ .

$\frac{x (5 \cdot 2 + 3)}{2} + 6 = \frac{5}{4} x$

Multiply $5$ by $2$ .

$\frac{x (10 + 3)}{2} + 6 = \frac{5}{4} x$

Add $10$ and $3$ .

$\frac{x \cdot 13}{2} + 6 = \frac{5}{4} x$

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

$\frac{13 x}{2} + 6 = \frac{5}{4} x$

Step 3

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

$\frac{13 x}{2} + 6 = \frac{5 x}{4}$

Step 4

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

Subtract $\frac{5 x}{4}$ from both sides of the equation.

$\frac{13 x}{2} + 6 - \frac{5 x}{4} = 0$

To write $\frac{13 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13 x}{2} \cdot \frac{2}{2} - \frac{5 x}{4} + 6 = 0$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{13 x}{2}$ by $\frac{2}{2}$ .

$\frac{13 x \cdot 2}{2 \cdot 2} - \frac{5 x}{4} + 6 = 0$

Multiply $2$ by $2$ .

$\frac{13 x \cdot 2}{4} - \frac{5 x}{4} + 6 = 0$

Combine the numerators over the common denominator.

$\frac{13 x \cdot 2 - 5 x}{4} + 6 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $13 x \cdot 2 - 5 x$ .

Factor $x$ out of $13 x \cdot 2$ .

$\frac{x (13 \cdot 2) - 5 x}{4} + 6 = 0$

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

$\frac{x (13 \cdot 2) + x \cdot - 5}{4} + 6 = 0$

Factor $x$ out of $x (13 \cdot 2) + x \cdot - 5$ .

$\frac{x (13 \cdot 2 - 5)}{4} + 6 = 0$

Multiply $13$ by $2$ .

$\frac{x (26 - 5)}{4} + 6 = 0$

Subtract $5$ from $26$ .

$\frac{x \cdot 21}{4} + 6 = 0$

Move $21$ to the left of $x$ .

$\frac{21 x}{4} + 6 = 0$

Step 5

Subtract $6$ from both sides of the equation.

$\frac{21 x}{4} = - 6$

Step 6

Multiply both sides of the equation by $\frac{4}{21}$ .

$\frac{4}{21} \cdot \frac{21 x}{4} = \frac{4}{21} \cdot - 6$

Step 7

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{21} \cdot \frac{21 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{21} \cdot \frac{21 x}{4} = \frac{4}{21} \cdot - 6$

Rewrite the expression.

$\frac{1}{21} (21 x) = \frac{4}{21} \cdot - 6$

Cancel the common factor of $21$ .

Factor $21$ out of $21 x$ .

$\frac{1}{21} (21 (x)) = \frac{4}{21} \cdot - 6$

Cancel the common factor.

$\frac{1}{21} (21 x) = \frac{4}{21} \cdot - 6$

Rewrite the expression.

$x = \frac{4}{21} \cdot - 6$

Simplify the right side.

Simplify $\frac{4}{21} \cdot - 6$ .

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$x = \frac{4}{3 (7)} \cdot - 6$

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{4}{7}$ and $- 2$ .

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

Simplify the expression.

Multiply $4$ by $- 2$ .

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

Move the negative in front of the fraction.

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.\overline{142857}$

Mixed Number Form:

$x = - 1 \frac{1}{7}$

Solve for x 5/4x=-(-5x-6)+3/2x

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