Algebra Examples

$\frac{1}{5} (15 b - 7) = 3 b - 9$

Step 1

Simplify $\frac{1}{5} \cdot (15 b - 7)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (15 b - 7) = 3 b - 9$

Step 1.2

Simplify by adding zeros.

$\frac{1}{5} \cdot (15 b - 7) = 3 b - 9$

Step 1.3

Apply the distributive property.

$\frac{1}{5} (15 b) + \frac{1}{5} \cdot - 7 = 3 b - 9$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Factor $5$ out of $15 b$ .

$\frac{1}{5} (5 (3 b)) + \frac{1}{5} \cdot - 7 = 3 b - 9$

Step 1.4.2

Cancel the common factor.

$\frac{1}{5} (5 (3 b)) + \frac{1}{5} \cdot - 7 = 3 b - 9$

Step 1.4.3

Rewrite the expression.

$3 b + \frac{1}{5} \cdot - 7 = 3 b - 9$

Step 1.5

Combine $\frac{1}{5}$ and $- 7$ .

$3 b + \frac{- 7}{5} = 3 b - 9$

Step 1.6

Move the negative in front of the fraction.

$3 b - \frac{7}{5} = 3 b - 9$

Step 2

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

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Step 2.1

Subtract $3 b$ from both sides of the equation.

$3 b - \frac{7}{5} - 3 b = - 9$

Step 2.2

Combine the opposite terms in $3 b - \frac{7}{5} - 3 b$ .

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Step 2.2.1

Subtract $3 b$ from $3 b$ .

$0 - \frac{7}{5} = - 9$

Step 2.2.2

Subtract $\frac{7}{5}$ from $0$ .

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

Step 3

Since $- \frac{7}{5} \neq - 9$ , there are no solutions.

No solution