Solve for x 1/4*(2x-14)=4

$\frac{1}{4} \cdot (2 x - 14) = 4$

Step 1

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cdot (2 x - 14)) = 4 \cdot 4$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $4 (\frac{1}{4} \cdot (2 x - 14))$ .

Apply the distributive property.

$4 (\frac{1}{4} (2 x) + \frac{1}{4} \cdot - 14) = 4 \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$4 (\frac{1}{2 (2)} (2 x) + \frac{1}{4} \cdot - 14) = 4 \cdot 4$

Factor $2$ out of $2 x$ .

$4 (\frac{1}{2 (2)} (2 (x)) + \frac{1}{4} \cdot - 14) = 4 \cdot 4$

Cancel the common factor.

$4 (\frac{1}{2 \cdot 2} (2 x) + \frac{1}{4} \cdot - 14) = 4 \cdot 4$

Rewrite the expression.

$4 (\frac{1}{2} x + \frac{1}{4} \cdot - 14) = 4 \cdot 4$

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

$4 (\frac{x}{2} + \frac{1}{4} \cdot - 14) = 4 \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$4 (\frac{x}{2} + \frac{1}{2 (2)} \cdot - 14) = 4 \cdot 4$

Factor $2$ out of $- 14$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{1}{2}$ and $- 7$ .

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

Move the negative in front of the fraction.

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x + 2 \cdot - 7 = 4 \cdot 4$

Multiply $2$ by $- 7$ .

$2 x - 14 = 4 \cdot 4$

Simplify the right side.

Multiply $4$ by $4$ .

$2 x - 14 = 16$

Step 3

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

Add $14$ to both sides of the equation.

$2 x = 16 + 14$

Add $16$ and $14$ .

$2 x = 30$

Step 4

Divide each term in $2 x = 30$ by $2$ and simplify.

Divide each term in $2 x = 30$ by $2$ .

$\frac{2 x}{2} = \frac{30}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{30}{2}$

Divide $x$ by $1$ .

$x = \frac{30}{2}$

Simplify the right side.

Divide $30$ by $2$ .

$x = 15$

Solve for x 1/4*(2x-14)=4

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