Basic Math Examples

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

Step 1

Multiply both sides by $7$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{9 b - 3}{7} \cdot 7$ .

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Step 2.1.1.1

Factor $3$ out of $9 b - 3$ .

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Step 2.1.1.1.1

Factor $3$ out of $9 b$ .

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

Step 2.1.1.1.2

Factor $3$ out of $- 3$ .

$\frac{3 (3 b) + 3 (- 1)}{7} \cdot 7 = (5 + 4 b) \cdot 7$

Step 2.1.1.1.3

Factor $3$ out of $3 (3 b) + 3 (- 1)$ .

$\frac{3 (3 b - 1)}{7} \cdot 7 = (5 + 4 b) \cdot 7$

Step 2.1.1.2

Cancel the common factor of $7$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{3 (3 b - 1)}{7} \cdot 7 = (5 + 4 b) \cdot 7$

Step 2.1.1.2.2

Rewrite the expression.

$3 (3 b - 1) = (5 + 4 b) \cdot 7$

Step 2.1.1.3

Apply the distributive property.

$3 (3 b) + 3 \cdot - 1 = (5 + 4 b) \cdot 7$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $3$ by $3$ .

$9 b + 3 \cdot - 1 = (5 + 4 b) \cdot 7$

Step 2.1.1.4.2

Multiply $3$ by $- 1$ .

$9 b - 3 = (5 + 4 b) \cdot 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(5 + 4 b) \cdot 7$ .

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Step 2.2.1.1

Apply the distributive property.

$9 b - 3 = 5 \cdot 7 + 4 b \cdot 7$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Multiply $5$ by $7$ .

$9 b - 3 = 35 + 4 b \cdot 7$

Step 2.2.1.2.2

Multiply $7$ by $4$ .

$9 b - 3 = 35 + 28 b$

Step 2.2.1.2.3

Reorder $35$ and $28 b$ .

$9 b - 3 = 28 b + 35$

Step 3

Solve for $b$ .

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Step 3.1

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

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Step 3.1.1

Subtract $28 b$ from both sides of the equation.

$9 b - 3 - 28 b = 35$

Step 3.1.2

Subtract $28 b$ from $9 b$ .

$- 19 b - 3 = 35$

Step 3.2

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

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Step 3.2.1

Add $3$ to both sides of the equation.

$- 19 b = 35 + 3$

Step 3.2.2

Add $35$ and $3$ .

$- 19 b = 38$

Step 3.3

Divide each term in $- 19 b = 38$ by $- 19$ and simplify.

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Step 3.3.1

Divide each term in $- 19 b = 38$ by $- 19$ .

$\frac{- 19 b}{- 19} = \frac{38}{- 19}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 19$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 19 b}{- 19} = \frac{38}{- 19}$

Step 3.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{38}{- 19}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $38$ by $- 19$ .

$b = - 2$