Algebra Examples

$\frac{3}{5} r + \frac{1}{5} r = - 15 + 11$

Step 1

Simplify $\frac{3}{5} r + \frac{1}{5} r$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{3 r}{5} + \frac{1}{5} r = - 15 + 11$

Step 1.1.2

Combine $\frac{1}{5}$ and $r$ .

$\frac{3 r}{5} + \frac{r}{5} = - 15 + 11$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{3 r + r}{5} = - 15 + 11$

Step 1.2.2

Add $3 r$ and $r$ .

$\frac{4 r}{5} = - 15 + 11$

Step 2

Add $- 15$ and $11$ .

$\frac{4 r}{5} = - 4$

Step 3

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 r}{5} = \frac{5}{4} \cdot - 4$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{5}{4} \cdot \frac{4 r}{5}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 r}{5} = \frac{5}{4} \cdot - 4$

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $4 r$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

$r = \frac{5}{4} \cdot - 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{5}{4} \cdot - 4$ .

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Factor $4$ out of $- 4$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

$r = 5 \cdot - 1$

Step 4.2.1.2

Multiply $5$ by $- 1$ .

$r = - 5$