Solve for x 1/2(3x+4)=5x

$\frac{1}{2} (3 x + 4) = 5 x$

Step 1

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

Start simplifying.

$0 + 0 + \frac{1}{2} \cdot (3 x + 4) = 5 x$

Simplify by adding zeros.

$\frac{1}{2} \cdot (3 x + 4) = 5 x$

Apply the distributive property.

$\frac{1}{2} (3 x) + \frac{1}{2} \cdot 4 = 5 x$

Multiply $\frac{1}{2} (3 x)$ .

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} x + \frac{1}{2} \cdot 4 = 5 x$

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

$\frac{3 x}{2} + \frac{1}{2} \cdot 4 = 5 x$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 x}{2} + \frac{1}{2} \cdot (2 (2)) = 5 x$

Cancel the common factor.

$\frac{3 x}{2} + \frac{1}{2} \cdot (2 \cdot 2) = 5 x$

Rewrite the expression.

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

Step 2

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

Subtract $5 x$ from both sides of the equation.

$\frac{3 x}{2} + 2 - 5 x = 0$

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

$\frac{3 x}{2} - 5 x \cdot \frac{2}{2} + 2 = 0$

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

$\frac{3 x}{2} + \frac{- 5 x \cdot 2}{2} + 2 = 0$

Combine the numerators over the common denominator.

$\frac{3 x - 5 x \cdot 2}{2} + 2 = 0$

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - 5 x \cdot 2}{2} + 2 = 0$

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

$\frac{x \cdot 3 + x (- 5 \cdot 2)}{2} + 2 = 0$

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

$\frac{x (3 - 5 \cdot 2)}{2} + 2 = 0$

Multiply $- 5$ by $2$ .

$\frac{x (3 - 10)}{2} + 2 = 0$

Subtract $10$ from $3$ .

$\frac{x \cdot - 7}{2} + 2 = 0$

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

$\frac{- 7 \cdot x}{2} + 2 = 0$

Move the negative in front of the fraction.

$- \frac{7 x}{2} + 2 = 0$

Step 3

Subtract $2$ from both sides of the equation.

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

Step 4

Multiply both sides of the equation by $- \frac{2}{7}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{7} (- \frac{7 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{7}$ into the numerator.

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

Move the leading negative in $- \frac{7 x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Multiply $- \frac{2}{7} \cdot - 2$ .

Multiply $- 2$ by $- 1$ .

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

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

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

Multiply $2$ by $2$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{571428}$

Solve for x 1/2(3x+4)=5x

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