Basic Math Examples

$\frac{7 g - 21}{3} - \frac{2 g - 7}{4} + 1 = 5 g - 2$

Step 1

Simplify $\frac{7 g - 21}{3} - \frac{2 g - 7}{4} + 1$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{7 g - 21}{3}$ by $\frac{4}{4}$ .

$\frac{7 g - 21}{3} \cdot \frac{4}{4} - \frac{2 g - 7}{4} + 1 = 5 g - 2$

Step 1.1.2

Multiply $\frac{7 g - 21}{3}$ by $\frac{4}{4}$ .

$\frac{(7 g - 21) \cdot 4}{3 \cdot 4} - \frac{2 g - 7}{4} + 1 = 5 g - 2$

Step 1.1.3

Multiply $\frac{2 g - 7}{4}$ by $\frac{3}{3}$ .

$\frac{(7 g - 21) \cdot 4}{3 \cdot 4} - (\frac{2 g - 7}{4} \cdot \frac{3}{3}) + 1 = 5 g - 2$

Step 1.1.4

Multiply $\frac{2 g - 7}{4}$ by $\frac{3}{3}$ .

$\frac{(7 g - 21) \cdot 4}{3 \cdot 4} - \frac{(2 g - 7) \cdot 3}{4 \cdot 3} + 1 = 5 g - 2$

Step 1.1.5

Write $1$ as a fraction with denominator $1$ .

$\frac{(7 g - 21) \cdot 4}{3 \cdot 4} - \frac{(2 g - 7) \cdot 3}{4 \cdot 3} + \frac{1}{1} = 5 g - 2$

Step 1.1.6

Multiply $\frac{1}{1}$ by $\frac{12}{12}$ .

$\frac{(7 g - 21) \cdot 4}{3 \cdot 4} - \frac{(2 g - 7) \cdot 3}{4 \cdot 3} + \frac{1}{1} \cdot \frac{12}{12} = 5 g - 2$

Step 1.1.7

Multiply $\frac{1}{1}$ by $\frac{12}{12}$ .

$\frac{(7 g - 21) \cdot 4}{3 \cdot 4} - \frac{(2 g - 7) \cdot 3}{4 \cdot 3} + \frac{12}{12} = 5 g - 2$

Step 1.1.8

Multiply $3$ by $4$ .

$\frac{(7 g - 21) \cdot 4}{12} - \frac{(2 g - 7) \cdot 3}{4 \cdot 3} + \frac{12}{12} = 5 g - 2$

Step 1.1.9

Reorder the factors of $4 \cdot 3$ .

$\frac{(7 g - 21) \cdot 4}{12} - \frac{(2 g - 7) \cdot 3}{3 \cdot 4} + \frac{12}{12} = 5 g - 2$

Step 1.1.10

Multiply $3$ by $4$ .

$\frac{(7 g - 21) \cdot 4}{12} - \frac{(2 g - 7) \cdot 3}{12} + \frac{12}{12} = 5 g - 2$

Step 1.2

Combine the numerators over the common denominator.

$\frac{(7 g - 21) \cdot 4 - (2 g - 7) \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{7 g \cdot 4 - 21 \cdot 4 - (2 g - 7) \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.2

Multiply $4$ by $7$ .

$\frac{28 g - 21 \cdot 4 - (2 g - 7) \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.3

Multiply $- 21$ by $4$ .

$\frac{28 g - 84 - (2 g - 7) \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.4

Apply the distributive property.

$\frac{28 g - 84 + (- (2 g) - - 7) \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.5

Multiply $2$ by $- 1$ .

$\frac{28 g - 84 + (- 2 g - - 7) \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.6

Multiply $- 1$ by $- 7$ .

$\frac{28 g - 84 + (- 2 g + 7) \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.7

Apply the distributive property.

$\frac{28 g - 84 - 2 g \cdot 3 + 7 \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.8

Multiply $3$ by $- 2$ .

$\frac{28 g - 84 - 6 g + 7 \cdot 3 + 12}{12} = 5 g - 2$

Step 1.3.9

Multiply $7$ by $3$ .

$\frac{28 g - 84 - 6 g + 21 + 12}{12} = 5 g - 2$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Subtract $6 g$ from $28 g$ .

$\frac{22 g - 84 + 21 + 12}{12} = 5 g - 2$

Step 1.4.2

Simplify by adding numbers.

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Step 1.4.2.1

Add $- 84$ and $21$ .

$\frac{22 g - 63 + 12}{12} = 5 g - 2$

Step 1.4.2.2

Add $- 63$ and $12$ .

$\frac{22 g - 51}{12} = 5 g - 2$

Step 2

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

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Step 2.1

Subtract $5 g$ from both sides of the equation.

$\frac{22 g - 51}{12} - 5 g = - 2$

Step 2.2

To write $- 5 g$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{22 g - 51}{12} - 5 g \cdot \frac{12}{12} = - 2$

Step 2.3

Combine $- 5 g$ and $\frac{12}{12}$ .

$\frac{22 g - 51}{12} + \frac{- 5 g \cdot 12}{12} = - 2$

Step 2.4

Combine the numerators over the common denominator.

$\frac{22 g - 51 - 5 g \cdot 12}{12} = - 2$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $12$ by $- 5$ .

$\frac{22 g - 51 - 60 g}{12} = - 2$

Step 2.5.2

Subtract $60 g$ from $22 g$ .

$\frac{- 38 g - 51}{12} = - 2$

Step 2.6

Factor $- 1$ out of $- 38 g$ .

$\frac{- (38 g) - 51}{12} = - 2$

Step 2.7

Rewrite $- 51$ as $- 1 (51)$ .

$\frac{- (38 g) - 1 (51)}{12} = - 2$

Step 2.8

Factor $- 1$ out of $- (38 g) - 1 (51)$ .

$\frac{- (38 g + 51)}{12} = - 2$

Step 2.9

Rewrite $- (38 g + 51)$ as $- 1 (38 g + 51)$ .

$\frac{- 1 (38 g + 51)}{12} = - 2$

Step 2.10

Move the negative in front of the fraction.

$- \frac{38 g + 51}{12} = - 2$

Step 3

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{38 g + 51}{12}) = - 12 \cdot - 2$

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 $- 12 (- \frac{38 g + 51}{12})$ .

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Step 4.1.1.1

Cancel the common factor of $12$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{38 g + 51}{12}$ into the numerator.

$- 12 \frac{- (38 g + 51)}{12} = - 12 \cdot - 2$

Step 4.1.1.1.2

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- (38 g + 51)}{12} = - 12 \cdot - 2$

Step 4.1.1.1.3

Cancel the common factor.

$12 \cdot - 1 \frac{- (38 g + 51)}{12} = - 12 \cdot - 2$

Step 4.1.1.1.4

Rewrite the expression.

$- - (38 g + 51) = - 12 \cdot - 2$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (38 g + 51) = - 12 \cdot - 2$

Step 4.1.1.2.2

Multiply $38 g + 51$ by $1$ .

$38 g + 51 = - 12 \cdot - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 12$ by $- 2$ .

$38 g + 51 = 24$

Step 5

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

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Step 5.1

Subtract $51$ from both sides of the equation.

$38 g = 24 - 51$

Step 5.2

Subtract $51$ from $24$ .

$38 g = - 27$

Step 6

Divide each term in $38 g = - 27$ by $38$ and simplify.

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Step 6.1

Divide each term in $38 g = - 27$ by $38$ .

$\frac{38 g}{38} = \frac{- 27}{38}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $38$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{38 g}{38} = \frac{- 27}{38}$

Step 6.2.1.2

Divide $g$ by $1$ .

$g = \frac{- 27}{38}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$g = - \frac{27}{38}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$g = - \frac{27}{38}$

Decimal Form:

$g = - 0.71052631 \dots$