Solve for x 1/4(8x-20)-16=10x+51

$\frac{1}{4} (8 x - 20) - 16 = 10 x + 51$

Step 1

Simplify $\frac{1}{4} \cdot (8 x - 20) - 16$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{4} (8 x) + \frac{1}{4} \cdot - 20 - 16 = 10 x + 51$

Cancel the common factor of $4$ .

Factor $4$ out of $8 x$ .

$\frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 20 - 16 = 10 x + 51$

Cancel the common factor.

$\frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 20 - 16 = 10 x + 51$

Rewrite the expression.

$2 x + \frac{1}{4} \cdot - 20 - 16 = 10 x + 51$

Cancel the common factor of $4$ .

Factor $4$ out of $- 20$ .

$2 x + \frac{1}{4} \cdot (4 (- 5)) - 16 = 10 x + 51$

Cancel the common factor.

$2 x + \frac{1}{4} \cdot (4 \cdot - 5) - 16 = 10 x + 51$

Rewrite the expression.

$2 x - 5 - 16 = 10 x + 51$

Subtract $16$ from $- 5$ .

$2 x - 21 = 10 x + 51$

Step 2

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

Subtract $10 x$ from both sides of the equation.

$2 x - 21 - 10 x = 51$

Subtract $10 x$ from $2 x$ .

$- 8 x - 21 = 51$

Step 3

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

Add $21$ to both sides of the equation.

$- 8 x = 51 + 21$

Add $51$ and $21$ .

$- 8 x = 72$

Step 4

Divide each term in $- 8 x = 72$ by $- 8$ and simplify.

Divide each term in $- 8 x = 72$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{72}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{72}{- 8}$

Divide $x$ by $1$ .

$x = \frac{72}{- 8}$

Simplify the right side.

Divide $72$ by $- 8$ .

$x = - 9$

Solve for x 1/4(8x-20)-16=10x+51

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