Basic Math Examples

$(- 5 g + 40) \div 3 = 2 g \div 2$

Step 1

Multiply both sides by $3$ .

$(- 5 g + 40) \div 3 \cdot 3 = 2 g \div 2 \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(- 5 g + 40) \div 3 \cdot 3$ .

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Step 2.1.1.1

Factor $5$ out of $- 5 g + 40$ .

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Step 2.1.1.1.1

Factor $5$ out of $- 5 g$ .

$(5 (- g) + 40) \div 3 \cdot 3 = 2 g \div 2 \cdot 3$

Step 2.1.1.1.2

Factor $5$ out of $40$ .

$(5 (- g) + 5 (8)) \div 3 \cdot 3 = 2 g \div 2 \cdot 3$

Step 2.1.1.1.3

Factor $5$ out of $5 (- g) + 5 (8)$ .

$5 (- g + 8) \div 3 \cdot 3 = 2 g \div 2 \cdot 3$

Step 2.1.1.2

Rewrite the division as a fraction.

$\frac{5 (- g + 8)}{3} \cdot 3 = 2 g \div 2 \cdot 3$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{5 (- g + 8)}{3} \cdot 3 = 2 g \div 2 \cdot 3$

Step 2.1.1.3.2

Rewrite the expression.

$5 (- g + 8) = 2 g \div 2 \cdot 3$

Step 2.1.1.4

Apply the distributive property.

$5 (- g) + 5 \cdot 8 = 2 g \div 2 \cdot 3$

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $- 1$ by $5$ .

$- 5 g + 5 \cdot 8 = 2 g \div 2 \cdot 3$

Step 2.1.1.5.2

Multiply $5$ by $8$ .

$- 5 g + 40 = 2 g \div 2 \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $2 g \div 2 \cdot 3$ .

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Step 2.2.1.1

Rewrite the division as a fraction.

$- 5 g + 40 = \frac{2 g}{2} \cdot 3$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Cancel the common factor.

$- 5 g + 40 = \frac{2 g}{2} \cdot 3$

Step 2.2.1.2.2

Divide $g$ by $1$ .

$- 5 g + 40 = g \cdot 3$

Step 2.2.1.3

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

$- 5 g + 40 = 3 g$

Step 3

Solve for $g$ .

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Step 3.1

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

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Step 3.1.1

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

$- 5 g + 40 - 3 g = 0$

Step 3.1.2

Subtract $3 g$ from $- 5 g$ .

$- 8 g + 40 = 0$

Step 3.2

Subtract $40$ from both sides of the equation.

$- 8 g = - 40$

Step 3.3

Divide each term in $- 8 g = - 40$ by $- 8$ and simplify.

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Step 3.3.1

Divide each term in $- 8 g = - 40$ by $- 8$ .

$\frac{- 8 g}{- 8} = \frac{- 40}{- 8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 8 g}{- 8} = \frac{- 40}{- 8}$

Step 3.3.2.1.2

Divide $g$ by $1$ .

$g = \frac{- 40}{- 8}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 40$ by $- 8$ .

$g = 5$