Solve for x (3x)/2+1/4(x-2)=10

$\frac{3 x}{2} + \frac{1}{4} (x - 2) = 10$

Simplify $\frac{3 x}{2} + \frac{1}{4} \cdot (x - 2)$ .

Simplify each term.

Apply the distributive property.

$\frac{3 x}{2} + \frac{1}{4} x + \frac{1}{4} \cdot - 2 = 10$

Combine $\frac{1}{4}$ and $x$ .

$\frac{3 x}{2} + \frac{x}{4} + \frac{1}{4} \cdot - 2 = 10$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 x}{2} + \frac{x}{4} + \frac{1}{2 (2)} \cdot - 2 = 10$

Factor $2$ out of $- 2$ .

$\frac{3 x}{2} + \frac{x}{4} + \frac{1}{2 \cdot 2} \cdot (2 \cdot - 1) = 10$

Cancel the common factor.

$\frac{3 x}{2} + \frac{x}{4} + \frac{1}{2 \cdot 2} \cdot (2 \cdot - 1) = 10$

Rewrite the expression.

$\frac{3 x}{2} + \frac{x}{4} + \frac{1}{2} \cdot - 1 = 10$

Combine $\frac{1}{2}$ and $- 1$ .

$\frac{3 x}{2} + \frac{x}{4} + \frac{- 1}{2} = 10$

Move the negative in front of the fraction.

$\frac{3 x}{2} + \frac{x}{4} - \frac{1}{2} = 10$

To write $\frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} \cdot \frac{2}{2} + \frac{x}{4} - \frac{1}{2} = 10$

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

Multiply $\frac{3 x}{2}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2}{2 \cdot 2} + \frac{x}{4} - \frac{1}{2} = 10$

Multiply $2$ by $2$ .

$\frac{3 x \cdot 2}{4} + \frac{x}{4} - \frac{1}{2} = 10$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 + x}{4} - \frac{1}{2} = 10$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x (3 \cdot 2) + x}{4} - \frac{1}{2} = 10$

Raise $x$ to the power of $1$ .

$\frac{x (3 \cdot 2) + x^{1}}{4} - \frac{1}{2} = 10$

Factor $x$ out of $x^{1}$ .

$\frac{x (3 \cdot 2) + x \cdot 1}{4} - \frac{1}{2} = 10$

Factor $x$ out of $x (3 \cdot 2) + x \cdot 1$ .

$\frac{x (3 \cdot 2 + 1)}{4} - \frac{1}{2} = 10$

Multiply $3$ by $2$ .

$\frac{x (6 + 1)}{4} - \frac{1}{2} = 10$

Add $6$ and $1$ .

$\frac{x \cdot 7}{4} - \frac{1}{2} = 10$

Move $7$ to the left of $x$ .

$\frac{7 x}{4} - \frac{1}{2} = 10$

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

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{7 x}{4} = 10 + \frac{1}{2}$

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 x}{4} = 10 \cdot \frac{2}{2} + \frac{1}{2}$

Combine $10$ and $\frac{2}{2}$ .

$\frac{7 x}{4} = \frac{10 \cdot 2}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{7 x}{4} = \frac{10 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $10$ by $2$ .

$\frac{7 x}{4} = \frac{20 + 1}{2}$

Add $20$ and $1$ .

$\frac{7 x}{4} = \frac{21}{2}$

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

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot \frac{21}{2}$

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.

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot \frac{21}{2}$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot \frac{21}{2}$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{4}{7} \cdot \frac{21}{2}$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot \frac{21}{2}$

Rewrite the expression.

$x = \frac{4}{7} \cdot \frac{21}{2}$

Simplify the right side.

Simplify $\frac{4}{7} \cdot \frac{21}{2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{7} \cdot \frac{21}{2}$

Cancel the common factor.

$x = \frac{2 \cdot 2}{7} \cdot \frac{21}{2}$

Rewrite the expression.

$x = \frac{2}{7} \cdot 21$

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 2 \cdot 3$

Multiply $2$ by $3$ .

$x = 6$

Solve for x (3x)/2+1/4(x-2)=10

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