Algebra Examples

$\frac{5}{4} x - 2 = - \frac{1}{4} x + 19$

Step 1

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

$\frac{5 x}{4} - 2 = - \frac{1}{4} x + 19$

Step 2

Combine $x$ and $\frac{1}{4}$ .

$\frac{5 x}{4} - 2 = - \frac{x}{4} + 19$

Step 3

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

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Step 3.1

Add $\frac{x}{4}$ to both sides of the equation.

$\frac{5 x}{4} - 2 + \frac{x}{4} = 19$

Step 3.2

Combine the numerators over the common denominator.

$- 2 + \frac{5 x + x}{4} = 19$

Step 3.3

Add $5 x$ and $x$ .

$- 2 + \frac{6 x}{4} = 19$

Step 3.4

Cancel the common factor of $6$ and $4$ .

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Step 3.4.1

Factor $2$ out of $6 x$ .

$- 2 + \frac{2 (3 x)}{4} = 19$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $4$ .

$- 2 + \frac{2 (3 x)}{2 (2)} = 19$

Step 3.4.2.2

Cancel the common factor.

$- 2 + \frac{2 (3 x)}{2 \cdot 2} = 19$

Step 3.4.2.3

Rewrite the expression.

$- 2 + \frac{3 x}{2} = 19$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$\frac{3 x}{2} = 19 + 2$

Step 4.2

Add $19$ and $2$ .

$\frac{3 x}{2} = 21$

Step 5

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

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 21$

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

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 21$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 21$

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot 21$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 21$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{2}{3} \cdot 21$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{2}{3} \cdot 21$ .

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Step 6.2.1.1

Cancel the common factor of $3$ .

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Step 6.2.1.1.1

Factor $3$ out of $21$ .

$x = \frac{2}{3} \cdot (3 (7))$

Step 6.2.1.1.2

Cancel the common factor.

$x = \frac{2}{3} \cdot (3 \cdot 7)$

Step 6.2.1.1.3

Rewrite the expression.

$x = 2 \cdot 7$

Step 6.2.1.2

Multiply $2$ by $7$ .

$x = 14$