Solve for x (4x-3)/5-(4-2x)/3=1

$\frac{4 x - 3}{5} - \frac{4 - 2 x}{3} = 1$

Step 1

Simplify $\frac{4 x - 3}{5} - \frac{4 - 2 x}{3}$ .

Factor $2$ out of $4 - 2 x$ .

Factor $2$ out of $4$ .

$\frac{4 x - 3}{5} - \frac{2 (2) - 2 x}{3} = 1$

Factor $2$ out of $- 2 x$ .

$\frac{4 x - 3}{5} - \frac{2 (2) + 2 (- x)}{3} = 1$

Factor $2$ out of $2 (2) + 2 (- x)$ .

$\frac{4 x - 3}{5} - \frac{2 (2 - x)}{3} = 1$

To write $\frac{4 x - 3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 x - 3}{5} \cdot \frac{3}{3} - \frac{2 (2 - x)}{3} = 1$

To write $- \frac{2 (2 - x)}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 x - 3}{5} \cdot \frac{3}{3} - \frac{2 (2 - x)}{3} \cdot \frac{5}{5} = 1$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x - 3}{5}$ by $\frac{3}{3}$ .

$\frac{(4 x - 3) \cdot 3}{5 \cdot 3} - \frac{2 (2 - x)}{3} \cdot \frac{5}{5} = 1$

Multiply $5$ by $3$ .

$\frac{(4 x - 3) \cdot 3}{15} - \frac{2 (2 - x)}{3} \cdot \frac{5}{5} = 1$

Multiply $\frac{2 (2 - x)}{3}$ by $\frac{5}{5}$ .

$\frac{(4 x - 3) \cdot 3}{15} - \frac{2 (2 - x) \cdot 5}{3 \cdot 5} = 1$

Multiply $3$ by $5$ .

$\frac{(4 x - 3) \cdot 3}{15} - \frac{2 (2 - x) \cdot 5}{15} = 1$

Combine the numerators over the common denominator.

$\frac{(4 x - 3) \cdot 3 - 2 (2 - x) \cdot 5}{15} = 1$

Simplify the numerator.

Apply the distributive property.

$\frac{4 x \cdot 3 - 3 \cdot 3 - 2 (2 - x) \cdot 5}{15} = 1$

Multiply $3$ by $4$ .

$\frac{12 x - 3 \cdot 3 - 2 (2 - x) \cdot 5}{15} = 1$

Multiply $- 3$ by $3$ .

$\frac{12 x - 9 - 2 (2 - x) \cdot 5}{15} = 1$

Apply the distributive property.

$\frac{12 x - 9 + (- 2 \cdot 2 - 2 (- x)) \cdot 5}{15} = 1$

Multiply $- 2$ by $2$ .

$\frac{12 x - 9 + (- 4 - 2 (- x)) \cdot 5}{15} = 1$

Multiply $- 1$ by $- 2$ .

$\frac{12 x - 9 + (- 4 + 2 x) \cdot 5}{15} = 1$

Apply the distributive property.

$\frac{12 x - 9 - 4 \cdot 5 + 2 x \cdot 5}{15} = 1$

Multiply $- 4$ by $5$ .

$\frac{12 x - 9 - 20 + 2 x \cdot 5}{15} = 1$

Multiply $5$ by $2$ .

$\frac{12 x - 9 - 20 + 10 x}{15} = 1$

Add $12 x$ and $10 x$ .

$\frac{22 x - 9 - 20}{15} = 1$

Subtract $20$ from $- 9$ .

$\frac{22 x - 29}{15} = 1$

Step 2

Multiply both sides by $15$ .

$\frac{22 x - 29}{15} \cdot 15 = 1 \cdot 15$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{22 x - 29}{15} \cdot 15 = 1 \cdot 15$

Rewrite the expression.

$22 x - 29 = 1 \cdot 15$

Simplify the right side.

Multiply $15$ by $1$ .

$22 x - 29 = 15$

Step 4

Solve for $x$ .

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

Add $29$ to both sides of the equation.

$22 x = 15 + 29$

Add $15$ and $29$ .

$22 x = 44$

Divide each term in $22 x = 44$ by $22$ and simplify.

Divide each term in $22 x = 44$ by $22$ .

$\frac{22 x}{22} = \frac{44}{22}$

Simplify the left side.

Cancel the common factor of $22$ .

Cancel the common factor.

$\frac{22 x}{22} = \frac{44}{22}$

Divide $x$ by $1$ .

$x = \frac{44}{22}$

Simplify the right side.

Divide $44$ by $22$ .

$x = 2$

Solve for x (4x-3)/5-(4-2x)/3=1

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