Algebra Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $- \frac{3}{5} (3 a)$ .

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Step 1.1.2.1

Multiply $3$ by $- 1$ .

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Multiply $- 3$ by $3$ .

$4 + \frac{- 9}{5} a - \frac{3}{5} \cdot 4 = 7$

Step 1.1.2.4

Combine $\frac{- 9}{5}$ and $a$ .

$4 + \frac{- 9 a}{5} - \frac{3}{5} \cdot 4 = 7$

Step 1.1.3

Multiply $- \frac{3}{5} \cdot 4$ .

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Step 1.1.3.1

Multiply $4$ by $- 1$ .

$4 + \frac{- 9 a}{5} - 4 (\frac{3}{5}) = 7$

Step 1.1.3.2

Combine $- 4$ and $\frac{3}{5}$ .

$4 + \frac{- 9 a}{5} + \frac{- 4 \cdot 3}{5} = 7$

Step 1.1.3.3

Multiply $- 4$ by $3$ .

$4 + \frac{- 9 a}{5} + \frac{- 12}{5} = 7$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Move the negative in front of the fraction.

$4 - \frac{9 a}{5} + \frac{- 12}{5} = 7$

Step 1.1.4.2

Move the negative in front of the fraction.

$4 - \frac{9 a}{5} - \frac{12}{5} = 7$

Step 1.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{9 a}{5} + 4 \cdot \frac{5}{5} - \frac{12}{5} = 7$

Step 1.3

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

$- \frac{9 a}{5} + \frac{4 \cdot 5}{5} - \frac{12}{5} = 7$

Step 1.4

Combine the numerators over the common denominator.

$- \frac{9 a}{5} + \frac{4 \cdot 5 - 12}{5} = 7$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $4$ by $5$ .

$- \frac{9 a}{5} + \frac{20 - 12}{5} = 7$

Step 1.5.2

Subtract $12$ from $20$ .

$- \frac{9 a}{5} + \frac{8}{5} = 7$

Step 2

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

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Step 2.1

Subtract $\frac{8}{5}$ from both sides of the equation.

$- \frac{9 a}{5} = 7 - \frac{8}{5}$

Step 2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{9 a}{5} = 7 \cdot \frac{5}{5} - \frac{8}{5}$

Step 2.3

Combine $7$ and $\frac{5}{5}$ .

$- \frac{9 a}{5} = \frac{7 \cdot 5}{5} - \frac{8}{5}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{9 a}{5} = \frac{7 \cdot 5 - 8}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $5$ .

$- \frac{9 a}{5} = \frac{35 - 8}{5}$

Step 2.5.2

Subtract $8$ from $35$ .

$- \frac{9 a}{5} = \frac{27}{5}$

Step 3

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

$- 9 a = 27$

Step 4

Divide each term in $- 9 a = 27$ by $- 9$ and simplify.

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Step 4.1

Divide each term in $- 9 a = 27$ by $- 9$ .

$\frac{- 9 a}{- 9} = \frac{27}{- 9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 9 a}{- 9} = \frac{27}{- 9}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{27}{- 9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $27$ by $- 9$ .

$a = - 3$