Pre-Algebra Examples

$- a - \frac{5}{4} \cdot (- \frac{8}{3} a + 1) = - \frac{19}{4}$

Step 1

Simplify $- a - \frac{5}{4} \cdot (- \frac{8}{3} a + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Combine $a$ and $\frac{8}{3}$ .

$- a - \frac{5}{4} \cdot (- \frac{a \cdot 8}{3} + 1) = - \frac{19}{4}$

Step 1.1.1.2

Move $8$ to the left of $a$ .

$- a - \frac{5}{4} \cdot (- \frac{8 a}{3} + 1) = - \frac{19}{4}$

Step 1.1.2

Apply the distributive property.

$- a - \frac{5}{4} (- \frac{8 a}{3}) - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.3

Cancel the common factor of $4$ .

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Step 1.1.3.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$- a + \frac{- 5}{4} (- \frac{8 a}{3}) - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.3.2

Move the leading negative in $- \frac{8 a}{3}$ into the numerator.

$- a + \frac{- 5}{4} \cdot \frac{- 8 a}{3} - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.3.3

Factor $4$ out of $- 8 a$ .

$- a + \frac{- 5}{4} \cdot \frac{4 (- 2 a)}{3} - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.3.4

Cancel the common factor.

$- a + \frac{- 5}{4} \cdot \frac{4 (- 2 a)}{3} - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.3.5

Rewrite the expression.

$- a - 5 \frac{- 2 a}{3} - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.4

Combine $- 5$ and $\frac{- 2 a}{3}$ .

$- a + \frac{- 5 (- 2 a)}{3} - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.5

Multiply $- 2$ by $- 5$ .

$- a + \frac{10 a}{3} - \frac{5}{4} \cdot 1 = - \frac{19}{4}$

Step 1.1.6

Multiply $- 1$ by $1$ .

$- a + \frac{10 a}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.2

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

$- a \cdot \frac{3}{3} + \frac{10 a}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $- a$ and $\frac{3}{3}$ .

$\frac{- a \cdot 3}{3} + \frac{10 a}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{- a \cdot 3 + 10 a}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $a$ out of $- a \cdot 3 + 10 a$ .

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Step 1.4.1.1.1

Factor $a$ out of $- a \cdot 3$ .

$\frac{a (- 1 \cdot 3) + 10 a}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.4.1.1.2

Factor $a$ out of $10 a$ .

$\frac{a (- 1 \cdot 3) + a \cdot 10}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.4.1.1.3

Factor $a$ out of $a (- 1 \cdot 3) + a \cdot 10$ .

$\frac{a (- 1 \cdot 3 + 10)}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.4.1.2

Multiply $- 1$ by $3$ .

$\frac{a (- 3 + 10)}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.4.1.3

Add $- 3$ and $10$ .

$\frac{a \cdot 7}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 1.4.2

Move $7$ to the left of $a$ .

$\frac{7 a}{3} - \frac{5}{4} = - \frac{19}{4}$

Step 2

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

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Step 2.1

Add $\frac{5}{4}$ to both sides of the equation.

$\frac{7 a}{3} = - \frac{19}{4} + \frac{5}{4}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{7 a}{3} = \frac{- 19 + 5}{4}$

Step 2.3

Add $- 19$ and $5$ .

$\frac{7 a}{3} = \frac{- 14}{4}$

Step 2.4

Cancel the common factor of $- 14$ and $4$ .

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Step 2.4.1

Factor $2$ out of $- 14$ .

$\frac{7 a}{3} = \frac{2 (- 7)}{4}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

$\frac{7 a}{3} = \frac{2 \cdot - 7}{2 \cdot 2}$

Step 2.4.2.2

Cancel the common factor.

$\frac{7 a}{3} = \frac{2 \cdot - 7}{2 \cdot 2}$

Step 2.4.2.3

Rewrite the expression.

$\frac{7 a}{3} = \frac{- 7}{2}$

Step 2.5

Move the negative in front of the fraction.

$\frac{7 a}{3} = - \frac{7}{2}$

Step 3

Multiply both sides of the equation by $\frac{3}{7}$ .

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

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 $\frac{3}{7} \cdot \frac{7 a}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 a) = \frac{3}{7} (- \frac{7}{2})$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 a$ .

$\frac{1}{7} (7 (a)) = \frac{3}{7} (- \frac{7}{2})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 a) = \frac{3}{7} (- \frac{7}{2})$

Step 4.1.1.2.3

Rewrite the expression.

$a = \frac{3}{7} (- \frac{7}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{7} (- \frac{7}{2})$ .

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Step 4.2.1.1

Cancel the common factor of $7$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$a = \frac{3}{7} \cdot \frac{- 7}{2}$

Step 4.2.1.1.2

Factor $7$ out of $- 7$ .

$a = \frac{3}{7} \cdot \frac{7 (- 1)}{2}$

Step 4.2.1.1.3

Cancel the common factor.

$a = \frac{3}{7} \cdot \frac{7 \cdot - 1}{2}$

Step 4.2.1.1.4

Rewrite the expression.

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

Step 4.2.1.2

Combine $3$ and $\frac{- 1}{2}$ .

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

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $3$ by $- 1$ .

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

Step 4.2.1.3.2

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = - 1.5$

Mixed Number Form:

$a = - 1 \frac{1}{2}$