Solve for x -8(3x-1/4)=2(9-7x)

$- 8 (3 x - \frac{1}{4}) = 2 (9 - 7 x)$

Step 1

Simplify $- 8 (3 x - \frac{1}{4})$ .

Start simplifying.

$0 + 0 - 8 (3 x - \frac{1}{4}) = 2 (9 - 7 x)$

Simplify by adding zeros.

$- 8 (3 x - \frac{1}{4}) = 2 (9 - 7 x)$

Apply the distributive property.

$- 8 (3 x) - 8 (- \frac{1}{4}) = 2 (9 - 7 x)$

Multiply $3$ by $- 8$ .

$- 24 x - 8 (- \frac{1}{4}) = 2 (9 - 7 x)$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- 24 x - 8 (\frac{- 1}{4}) = 2 (9 - 7 x)$

Factor $4$ out of $- 8$ .

$- 24 x + 4 (- 2) \frac{- 1}{4} = 2 (9 - 7 x)$

Cancel the common factor.

$- 24 x + 4 \cdot - 2 \frac{- 1}{4} = 2 (9 - 7 x)$

Rewrite the expression.

$- 24 x - 2 \cdot - 1 = 2 (9 - 7 x)$

Multiply $- 2$ by $- 1$ .

$- 24 x + 2 = 2 (9 - 7 x)$

Step 2

Simplify $2 (9 - 7 x)$ .

Apply the distributive property.

$- 24 x + 2 = 2 \cdot 9 + 2 (- 7 x)$

Multiply.

Multiply $2$ by $9$ .

$- 24 x + 2 = 18 + 2 (- 7 x)$

Multiply $- 7$ by $2$ .

$- 24 x + 2 = 18 - 14 x$

Step 3

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

Add $14 x$ to both sides of the equation.

$- 24 x + 2 + 14 x = 18$

Add $- 24 x$ and $14 x$ .

$- 10 x + 2 = 18$

Step 4

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

Subtract $2$ from both sides of the equation.

$- 10 x = 18 - 2$

Subtract $2$ from $18$ .

$- 10 x = 16$

Step 5

Divide each term in $- 10 x = 16$ by $- 10$ and simplify.

Divide each term in $- 10 x = 16$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{16}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{16}{- 10}$

Divide $x$ by $1$ .

$x = \frac{16}{- 10}$

Simplify the right side.

Cancel the common factor of $16$ and $- 10$ .

Factor $2$ out of $16$ .

$x = \frac{2 (8)}{- 10}$

Cancel the common factors.

Factor $2$ out of $- 10$ .

$x = \frac{2 \cdot 8}{2 \cdot - 5}$

Cancel the common factor.

$x = \frac{2 \cdot 8}{2 \cdot - 5}$

Rewrite the expression.

$x = \frac{8}{- 5}$

Move the negative in front of the fraction.

$x = - \frac{8}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{5}$

Decimal Form:

$x = - 1.6$

Mixed Number Form:

$x = - 1 \frac{3}{5}$

Solve for x -8(3x-1/4)=2(9-7x)

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