Solve for x 3/8(2x-3)=1/4-x

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

Step 1

Simplify $\frac{3}{8} \cdot (2 x - 3)$ .

Rewrite.

$0 + 0 + \frac{3}{8} \cdot (2 x - 3) = \frac{1}{4} - x$

Simplify by adding zeros.

$\frac{3}{8} \cdot (2 x - 3) = \frac{1}{4} - x$

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{4} x + \frac{3}{8} \cdot - 3 = \frac{1}{4} - x$

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

$\frac{3 x}{4} + \frac{3}{8} \cdot - 3 = \frac{1}{4} - x$

Multiply $\frac{3}{8} \cdot - 3$ .

Combine $\frac{3}{8}$ and $- 3$ .

$\frac{3 x}{4} + \frac{3 \cdot - 3}{8} = \frac{1}{4} - x$

Multiply $3$ by $- 3$ .

$\frac{3 x}{4} + \frac{- 9}{8} = \frac{1}{4} - x$

Move the negative in front of the fraction.

$\frac{3 x}{4} - \frac{9}{8} = \frac{1}{4} - x$

Step 2

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

Add $x$ to both sides of the equation.

$\frac{3 x}{4} - \frac{9}{8} + x = \frac{1}{4}$

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

$\frac{3 x}{4} + x \cdot \frac{4}{4} - \frac{9}{8} = \frac{1}{4}$

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

$\frac{3 x}{4} + \frac{x \cdot 4}{4} - \frac{9}{8} = \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{3 x + x \cdot 4}{4} - \frac{9}{8} = \frac{1}{4}$

Add $3 x$ and $x \cdot 4$ .

Reorder $x$ and $4$ .

$\frac{3 x + 4 \cdot x}{4} - \frac{9}{8} = \frac{1}{4}$

Add $3 x$ and $4 \cdot x$ .

$\frac{7 x}{4} - \frac{9}{8} = \frac{1}{4}$

Step 3

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

Add $\frac{9}{8}$ to both sides of the equation.

$\frac{7 x}{4} = \frac{1}{4} + \frac{9}{8}$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 x}{4} = \frac{1}{4} \cdot \frac{2}{2} + \frac{9}{8}$

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

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{7 x}{4} = \frac{2}{4 \cdot 2} + \frac{9}{8}$

Multiply $4$ by $2$ .

$\frac{7 x}{4} = \frac{2}{8} + \frac{9}{8}$

Combine the numerators over the common denominator.

$\frac{7 x}{4} = \frac{2 + 9}{8}$

Add $2$ and $9$ .

$\frac{7 x}{4} = \frac{11}{8}$

Step 4

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot \frac{11}{8}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{7} \cdot \frac{7 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot \frac{11}{8}$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot \frac{11}{8}$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{4}{7} \cdot \frac{11}{8}$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot \frac{11}{8}$

Rewrite the expression.

$x = \frac{4}{7} \cdot \frac{11}{8}$

Simplify the right side.

Simplify $\frac{4}{7} \cdot \frac{11}{8}$ .

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$x = \frac{4}{7} \cdot \frac{11}{4 (2)}$

Cancel the common factor.

$x = \frac{4}{7} \cdot \frac{11}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{7} \cdot \frac{11}{2}$

Multiply $\frac{1}{7}$ by $\frac{11}{2}$ .

$x = \frac{11}{7 \cdot 2}$

Multiply $7$ by $2$ .

$x = \frac{11}{14}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{14}$

Decimal Form:

$x = 0.7\overline{857142}$

Solve for x 3/8(2x-3)=1/4-x

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