Algebra Examples

$\frac{5}{3} x = 2 x - \frac{2}{3} x + 2$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 x - \frac{2}{3} x + 2 = \frac{5}{3} x$

Step 2

Simplify $2 x - \frac{2}{3} x + 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $x$ and $\frac{2}{3}$ .

$2 x - \frac{x \cdot 2}{3} + 2 = \frac{5}{3} x$

Step 2.1.2

Move $2$ to the left of $x$ .

$2 x - \frac{2 x}{3} + 2 = \frac{5}{3} x$

Step 2.2

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

$2 x \cdot \frac{3}{3} - \frac{2 x}{3} + 2 = \frac{5}{3} x$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $2 x$ and $\frac{3}{3}$ .

$\frac{2 x \cdot 3}{3} - \frac{2 x}{3} + 2 = \frac{5}{3} x$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 - 2 x}{3} + 2 = \frac{5}{3} x$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Factor $2 x$ out of $2 x \cdot 3 - 2 x$ .

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Step 2.4.1.1

Factor $2 x$ out of $2 x \cdot 3$ .

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

Step 2.4.1.2

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

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

Step 2.4.1.3

Factor $2 x$ out of $2 x (3) + 2 x (- 1)$ .

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

Step 2.4.2

Subtract $1$ from $3$ .

$\frac{2 x \cdot 2}{3} + 2 = \frac{5}{3} x$

Step 2.4.3

Multiply $2$ by $2$ .

$\frac{4 x}{3} + 2 = \frac{5}{3} x$

Step 3

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

$\frac{4 x}{3} + 2 = \frac{5 x}{3}$

Step 4

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

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Step 4.1

Subtract $\frac{5 x}{3}$ from both sides of the equation.

$\frac{4 x}{3} + 2 - \frac{5 x}{3} = 0$

Step 4.2

Combine the numerators over the common denominator.

$2 + \frac{4 x - 5 x}{3} = 0$

Step 4.3

Subtract $5 x$ from $4 x$ .

$2 + \frac{- x}{3} = 0$

Step 4.4

Move the negative in front of the fraction.

$2 - \frac{x}{3} = 0$

Step 5

Subtract $2$ from both sides of the equation.

$- \frac{x}{3} = - 2$

Step 6

Multiply both sides of the equation by $- 3$ .

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

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

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

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Step 7.1.1.1

Cancel the common factor of $3$ .

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Step 7.1.1.1.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 3 \frac{- x}{3} = - 3 \cdot - 2$

Step 7.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 7.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 \cdot - 2$

Step 7.1.1.1.4

Rewrite the expression.

$- - x = - 3 \cdot - 2$

Step 7.1.1.2

Multiply.

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Step 7.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot - 2$

Step 7.1.1.2.2

Multiply $x$ by $1$ .

$x = - 3 \cdot - 2$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $- 3$ by $- 2$ .

$x = 6$