Solve for x 10x-(8x-3)/4=2(x-3)

$10 x - \frac{8 x - 3}{4} = 2 (x - 3)$

Step 1

Simplify $10 x - \frac{8 x - 3}{4}$ .

To write $10 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$10 x \cdot \frac{4}{4} - \frac{8 x - 3}{4} = 2 (x - 3)$

Simplify terms.

Combine $10 x$ and $\frac{4}{4}$ .

$\frac{10 x \cdot 4}{4} - \frac{8 x - 3}{4} = 2 (x - 3)$

Combine the numerators over the common denominator.

$\frac{10 x \cdot 4 - (8 x - 3)}{4} = 2 (x - 3)$

Simplify the numerator.

Multiply $4$ by $10$ .

$\frac{40 x - (8 x - 3)}{4} = 2 (x - 3)$

Apply the distributive property.

$\frac{40 x - (8 x) - - 3}{4} = 2 (x - 3)$

Multiply $8$ by $- 1$ .

$\frac{40 x - 8 x - - 3}{4} = 2 (x - 3)$

Multiply $- 1$ by $- 3$ .

$\frac{40 x - 8 x + 3}{4} = 2 (x - 3)$

Subtract $8 x$ from $40 x$ .

$\frac{32 x + 3}{4} = 2 (x - 3)$

Step 2

Simplify $2 (x - 3)$ .

Apply the distributive property.

$\frac{32 x + 3}{4} = 2 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$\frac{32 x + 3}{4} = 2 x - 6$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$\frac{32 x + 3}{4} - 2 x = - 6$

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{32 x + 3}{4} - 2 x \cdot \frac{4}{4} = - 6$

Combine $- 2 x$ and $\frac{4}{4}$ .

$\frac{32 x + 3}{4} + \frac{- 2 x \cdot 4}{4} = - 6$

Combine the numerators over the common denominator.

$\frac{32 x + 3 - 2 x \cdot 4}{4} = - 6$

Simplify the numerator.

Multiply $4$ by $- 2$ .

$\frac{32 x + 3 - 8 x}{4} = - 6$

Subtract $8 x$ from $32 x$ .

$\frac{24 x + 3}{4} = - 6$

Factor $3$ out of $24 x + 3$ .

Factor $3$ out of $24 x$ .

$\frac{3 (8 x) + 3}{4} = - 6$

Factor $3$ out of $3$ .

$\frac{3 (8 x) + 3 (1)}{4} = - 6$

Factor $3$ out of $3 (8 x) + 3 (1)$ .

$\frac{3 (8 x + 1)}{4} = - 6$

Step 4

Multiply both sides by $4$ .

$\frac{3 (8 x + 1)}{4} \cdot 4 = - 6 \cdot 4$

Step 5

Simplify.

Simplify the left side.

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

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 (8 x + 1)}{4} \cdot 4 = - 6 \cdot 4$

Rewrite the expression.

$3 (8 x + 1) = - 6 \cdot 4$

Apply the distributive property.

$3 (8 x) + 3 \cdot 1 = - 6 \cdot 4$

Multiply.

Multiply $8$ by $3$ .

$24 x + 3 \cdot 1 = - 6 \cdot 4$

Multiply $3$ by $1$ .

$24 x + 3 = - 6 \cdot 4$

Simplify the right side.

Multiply $- 6$ by $4$ .

$24 x + 3 = - 24$

Step 6

Solve for $x$ .

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

Subtract $3$ from both sides of the equation.

$24 x = - 24 - 3$

Subtract $3$ from $- 24$ .

$24 x = - 27$

Divide each term in $24 x = - 27$ by $24$ and simplify.

Divide each term in $24 x = - 27$ by $24$ .

$\frac{24 x}{24} = \frac{- 27}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 x}{24} = \frac{- 27}{24}$

Divide $x$ by $1$ .

$x = \frac{- 27}{24}$

Simplify the right side.

Cancel the common factor of $- 27$ and $24$ .

Factor $3$ out of $- 27$ .

$x = \frac{3 (- 9)}{24}$

Cancel the common factors.

Factor $3$ out of $24$ .

$x = \frac{3 \cdot - 9}{3 \cdot 8}$

Cancel the common factor.

$x = \frac{3 \cdot - 9}{3 \cdot 8}$

Rewrite the expression.

$x = \frac{- 9}{8}$

Move the negative in front of the fraction.

$x = - \frac{9}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{9}{8}$

Decimal Form:

$x = - 1.125$

Mixed Number Form:

$x = - 1 \frac{1}{8}$

Solve for x 10x-(8x-3)/4=2(x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.