Algebra Examples

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

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.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Simplify terms.

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Step 2.3.1

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

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

Step 2.3.2

Combine the numerators over the common denominator.

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

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $2 x$ out of $2 x - 4 x \cdot 3$ .

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Step 2.4.1.1.1

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

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

Step 2.4.1.1.2

Factor $2 x$ out of $- 4 x \cdot 3$ .

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

Step 2.4.1.1.3

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

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

Step 2.4.1.2

Multiply $- 2$ by $3$ .

$\frac{2 x (1 - 6)}{3} + 2 = - 4 x$

Step 2.4.1.3

Subtract $6$ from $1$ .

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

Step 2.4.1.4

Multiply $- 5$ by $2$ .

$\frac{- 10 x}{3} + 2 = - 4 x$

Step 2.4.2

Move the negative in front of the fraction.

$- \frac{10 x}{3} + 2 = - 4 x$

Step 3

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

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Step 3.1

Add $4 x$ to both sides of the equation.

$- \frac{10 x}{3} + 2 + 4 x = 0$

Step 3.2

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

$- \frac{10 x}{3} + 4 x \cdot \frac{3}{3} + 2 = 0$

Step 3.3

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

$- \frac{10 x}{3} + \frac{4 x \cdot 3}{3} + 2 = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- 10 x + 4 x \cdot 3}{3} + 2 = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $2 x$ out of $- 10 x + 4 x \cdot 3$ .

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Step 3.5.1.1

Factor $2 x$ out of $- 10 x$ .

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

Step 3.5.1.2

Factor $2 x$ out of $4 x \cdot 3$ .

$\frac{2 x (- 5) + 2 x (2 \cdot 3)}{3} + 2 = 0$

Step 3.5.1.3

Factor $2 x$ out of $2 x (- 5) + 2 x (2 \cdot 3)$ .

$\frac{2 x (- 5 + 2 \cdot 3)}{3} + 2 = 0$

Step 3.5.2

Multiply $2$ by $3$ .

$\frac{2 x (- 5 + 6)}{3} + 2 = 0$

Step 3.5.3

Add $- 5$ and $6$ .

$\frac{2 x \cdot 1}{3} + 2 = 0$

Step 3.5.4

Multiply $2$ by $1$ .

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

Step 4

Subtract $2$ from both sides of the equation.

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

Step 5

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Cancel the common factor.

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

Step 6.1.1.1.2

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of $2$ .

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Step 6.1.1.2.1

Factor $2$ out of $2 x$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{3}{2} \cdot - 2$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Factor $2$ out of $- 2$ .

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

Step 6.2.1.1.2

Cancel the common factor.

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

Step 6.2.1.1.3

Rewrite the expression.

$x = 3 \cdot - 1$

Step 6.2.1.2

Multiply $3$ by $- 1$ .

$x = - 3$