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

$\frac{3 x}{8} - \frac{4 x}{3} = 4$

Step 1

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

To write $\frac{3 x}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{8} \cdot \frac{3}{3} - \frac{4 x}{3} = 4$

To write $- \frac{4 x}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3 x}{8} \cdot \frac{3}{3} - \frac{4 x}{3} \cdot \frac{8}{8} = 4$

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{8}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 3}{8 \cdot 3} - \frac{4 x}{3} \cdot \frac{8}{8} = 4$

Multiply $8$ by $3$ .

$\frac{3 x \cdot 3}{24} - \frac{4 x}{3} \cdot \frac{8}{8} = 4$

Multiply $\frac{4 x}{3}$ by $\frac{8}{8}$ .

$\frac{3 x \cdot 3}{24} - \frac{4 x \cdot 8}{3 \cdot 8} = 4$

Multiply $3$ by $8$ .

$\frac{3 x \cdot 3}{24} - \frac{4 x \cdot 8}{24} = 4$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - 4 x \cdot 8}{24} = 4$

Simplify the numerator.

Factor $x$ out of $3 x \cdot 3 - 4 x \cdot 8$ .

Factor $x$ out of $3 x \cdot 3$ .

$\frac{x (3 \cdot 3) - 4 x \cdot 8}{24} = 4$

Factor $x$ out of $- 4 x \cdot 8$ .

$\frac{x (3 \cdot 3) + x (- 4 \cdot 8)}{24} = 4$

Factor $x$ out of $x (3 \cdot 3) + x (- 4 \cdot 8)$ .

$\frac{x (3 \cdot 3 - 4 \cdot 8)}{24} = 4$

Multiply $3$ by $3$ .

$\frac{x (9 - 4 \cdot 8)}{24} = 4$

Multiply $- 4$ by $8$ .

$\frac{x (9 - 32)}{24} = 4$

Subtract $32$ from $9$ .

$\frac{x \cdot - 23}{24} = 4$

Simplify the expression.

Move $- 23$ to the left of $x$ .

$\frac{- 23 \cdot x}{24} = 4$

Move the negative in front of the fraction.

$- \frac{23 x}{24} = 4$

Step 2

Multiply both sides of the equation by $- \frac{24}{23}$ .

$- \frac{24}{23} (- \frac{23 x}{24}) = - \frac{24}{23} \cdot 4$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{24}{23} (- \frac{23 x}{24})$ .

Cancel the common factor of $24$ .

Move the leading negative in $- \frac{24}{23}$ into the numerator.

$\frac{- 24}{23} (- \frac{23 x}{24}) = - \frac{24}{23} \cdot 4$

Move the leading negative in $- \frac{23 x}{24}$ into the numerator.

$\frac{- 24}{23} \cdot \frac{- 23 x}{24} = - \frac{24}{23} \cdot 4$

Factor $24$ out of $- 24$ .

$\frac{24 (- 1)}{23} \cdot \frac{- 23 x}{24} = - \frac{24}{23} \cdot 4$

Cancel the common factor.

$\frac{24 \cdot - 1}{23} \cdot \frac{- 23 x}{24} = - \frac{24}{23} \cdot 4$

Rewrite the expression.

$\frac{- 1}{23} (- 23 x) = - \frac{24}{23} \cdot 4$

Cancel the common factor of $23$ .

Factor $23$ out of $- 23 x$ .

$\frac{- 1}{23} (23 (- x)) = - \frac{24}{23} \cdot 4$

Cancel the common factor.

$\frac{- 1}{23} (23 (- x)) = - \frac{24}{23} \cdot 4$

Rewrite the expression.

$- - x = - \frac{24}{23} \cdot 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{24}{23} \cdot 4$

Multiply $x$ by $1$ .

$x = - \frac{24}{23} \cdot 4$

Simplify the right side.

Simplify $- \frac{24}{23} \cdot 4$ .

Multiply $- \frac{24}{23} \cdot 4$ .

Multiply $4$ by $- 1$ .

$x = - 4 (\frac{24}{23})$

Combine $- 4$ and $\frac{24}{23}$ .

$x = \frac{- 4 \cdot 24}{23}$

Multiply $- 4$ by $24$ .

$x = \frac{- 96}{23}$

Move the negative in front of the fraction.

$x = - \frac{96}{23}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{96}{23}$

Decimal Form:

$x = - 4.17391304 \dots$

Mixed Number Form:

$x = - 4 \frac{4}{23}$

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

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