Algebra Examples

$\frac{61}{28} + a = \frac{19}{4} a - \frac{11}{7}$

Step 1

Combine $\frac{19}{4}$ and $a$ .

$\frac{61}{28} + a = \frac{19 a}{4} - \frac{11}{7}$

Step 2

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

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Step 2.1

Subtract $\frac{19 a}{4}$ from both sides of the equation.

$\frac{61}{28} + a - \frac{19 a}{4} = - \frac{11}{7}$

Step 2.2

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

$\frac{61}{28} + a \cdot \frac{4}{4} - \frac{19 a}{4} = - \frac{11}{7}$

Step 2.3

Combine $a$ and $\frac{4}{4}$ .

$\frac{61}{28} + \frac{a \cdot 4}{4} - \frac{19 a}{4} = - \frac{11}{7}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{61}{28} + \frac{a \cdot 4 - 19 a}{4} = - \frac{11}{7}$

Step 2.5

Subtract $19 a$ from $a \cdot 4$ .

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Step 2.5.1

Reorder $a$ and $4$ .

$\frac{61}{28} + \frac{4 \cdot a - 19 a}{4} = - \frac{11}{7}$

Step 2.5.2

Subtract $19 a$ from $4 \cdot a$ .

$\frac{61}{28} + \frac{- 15 \cdot a}{4} = - \frac{11}{7}$

Step 2.6

Move the negative in front of the fraction.

$\frac{61}{28} - \frac{15 a}{4} = - \frac{11}{7}$

Step 3

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

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Step 3.1

Subtract $\frac{61}{28}$ from both sides of the equation.

$- \frac{15 a}{4} = - \frac{11}{7} - \frac{61}{28}$

Step 3.2

To write $- \frac{11}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{15 a}{4} = - \frac{11}{7} \cdot \frac{4}{4} - \frac{61}{28}$

Step 3.3

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{11}{7}$ by $\frac{4}{4}$ .

$- \frac{15 a}{4} = - \frac{11 \cdot 4}{7 \cdot 4} - \frac{61}{28}$

Step 3.3.2

Multiply $7$ by $4$ .

$- \frac{15 a}{4} = - \frac{11 \cdot 4}{28} - \frac{61}{28}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{15 a}{4} = \frac{- 11 \cdot 4 - 61}{28}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 11$ by $4$ .

$- \frac{15 a}{4} = \frac{- 44 - 61}{28}$

Step 3.5.2

Subtract $61$ from $- 44$ .

$- \frac{15 a}{4} = \frac{- 105}{28}$

Step 3.6

Cancel the common factor of $- 105$ and $28$ .

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Step 3.6.1

Factor $7$ out of $- 105$ .

$- \frac{15 a}{4} = \frac{7 (- 15)}{28}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $7$ out of $28$ .

$- \frac{15 a}{4} = \frac{7 \cdot - 15}{7 \cdot 4}$

Step 3.6.2.2

Cancel the common factor.

$- \frac{15 a}{4} = \frac{7 \cdot - 15}{7 \cdot 4}$

Step 3.6.2.3

Rewrite the expression.

$- \frac{15 a}{4} = \frac{- 15}{4}$

Step 3.7

Move the negative in front of the fraction.

$- \frac{15 a}{4} = - \frac{15}{4}$

Step 4

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

$- 15 a = - 15$

Step 5

Divide each term in $- 15 a = - 15$ by $- 15$ and simplify.

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Step 5.1

Divide each term in $- 15 a = - 15$ by $- 15$ .

$\frac{- 15 a}{- 15} = \frac{- 15}{- 15}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 15$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 15 a}{- 15} = \frac{- 15}{- 15}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 15}{- 15}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 15$ by $- 15$ .

$a = 1$