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

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

Step 1

Simplify $\frac{5}{3} \cdot (4 x - 5)$ .

Rewrite.

$0 + 0 + \frac{5}{3} \cdot (4 x - 5) = 4 x - \frac{1}{3}$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $\frac{5}{3} (4 x)$ .

Combine $4$ and $\frac{5}{3}$ .

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

Multiply $4$ by $5$ .

$\frac{20}{3} x + \frac{5}{3} \cdot - 5 = 4 x - \frac{1}{3}$

Combine $\frac{20}{3}$ and $x$ .

$\frac{20 x}{3} + \frac{5}{3} \cdot - 5 = 4 x - \frac{1}{3}$

Multiply $\frac{5}{3} \cdot - 5$ .

Combine $\frac{5}{3}$ and $- 5$ .

$\frac{20 x}{3} + \frac{5 \cdot - 5}{3} = 4 x - \frac{1}{3}$

Multiply $5$ by $- 5$ .

$\frac{20 x}{3} + \frac{- 25}{3} = 4 x - \frac{1}{3}$

Move the negative in front of the fraction.

$\frac{20 x}{3} - \frac{25}{3} = 4 x - \frac{1}{3}$

Step 2

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

Subtract $4 x$ from both sides of the equation.

$\frac{20 x}{3} - \frac{25}{3} - 4 x = - \frac{1}{3}$

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

$\frac{20 x}{3} - 4 x \cdot \frac{3}{3} - \frac{25}{3} = - \frac{1}{3}$

Combine $- 4 x$ and $\frac{3}{3}$ .

$\frac{20 x}{3} + \frac{- 4 x \cdot 3}{3} - \frac{25}{3} = - \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{20 x - 4 x \cdot 3}{3} - \frac{25}{3} = - \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{20 x - 4 x \cdot 3 - 25}{3} = - \frac{1}{3}$

Multiply $3$ by $- 4$ .

$\frac{20 x - 12 x - 25}{3} = - \frac{1}{3}$

Subtract $12 x$ from $20 x$ .

$\frac{8 x - 25}{3} = - \frac{1}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$8 x - 25 = - 1$

Step 4

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

Add $25$ to both sides of the equation.

$8 x = - 1 + 25$

Add $- 1$ and $25$ .

$8 x = 24$

Step 5

Divide each term in $8 x = 24$ by $8$ and simplify.

Divide each term in $8 x = 24$ by $8$ .

$\frac{8 x}{8} = \frac{24}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{24}{8}$

Divide $x$ by $1$ .

$x = \frac{24}{8}$

Simplify the right side.

Divide $24$ by $8$ .

$x = 3$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.