Pre-Algebra Examples

$- \frac{3}{5} b + 7 + \frac{2}{5} b = 19$

Step 1

Simplify $- \frac{3}{5} b + 7 + \frac{2}{5} b$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$- \frac{b \cdot 3}{5} + 7 + \frac{2}{5} b = 19$

Step 1.1.2

Move $3$ to the left of $b$ .

$- \frac{3 \cdot b}{5} + 7 + \frac{2}{5} b = 19$

Step 1.1.3

Combine $\frac{2}{5}$ and $b$ .

$- \frac{3 b}{5} + 7 + \frac{2 b}{5} = 19$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$7 + \frac{- 3 b + 2 b}{5} = 19$

Step 1.2.2

Add $- 3 b$ and $2 b$ .

$7 + \frac{- b}{5} = 19$

Step 1.2.3

Move the negative in front of the fraction.

$7 - \frac{b}{5} = 19$

Step 2

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

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Step 2.1

Subtract $7$ from both sides of the equation.

$- \frac{b}{5} = 19 - 7$

Step 2.2

Subtract $7$ from $19$ .

$- \frac{b}{5} = 12$

Step 3

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{b}{5}) = - 5 \cdot 12$

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 $- 5 (- \frac{b}{5})$ .

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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

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

$- 5 \frac{- b}{5} = - 5 \cdot 12$

Step 4.1.1.1.2

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- b}{5} = - 5 \cdot 12$

Step 4.1.1.1.3

Cancel the common factor.

$5 \cdot - 1 \frac{- b}{5} = - 5 \cdot 12$

Step 4.1.1.1.4

Rewrite the expression.

$- - b = - 5 \cdot 12$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 b = - 5 \cdot 12$

Step 4.1.1.2.2

Multiply $b$ by $1$ .

$b = - 5 \cdot 12$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 5$ by $12$ .

$b = - 60$