Algebra Examples

$2 - \frac{3}{2} (4 g - 2) = - \frac{1}{5} (5 g + 10) - g$

Step 1

Since $g$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \frac{1}{5} \cdot (5 g + 10) - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2

Simplify $- \frac{1}{5} \cdot (5 g + 10) - g$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- \frac{1}{5} (5 g) - \frac{1}{5} \cdot 10 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.2

Cancel the common factor of $5$ .

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Step 2.1.2.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{- 1}{5} (5 g) - \frac{1}{5} \cdot 10 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.2.2

Factor $5$ out of $5 g$ .

$\frac{- 1}{5} (5 (g)) - \frac{1}{5} \cdot 10 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.2.3

Cancel the common factor.

$\frac{- 1}{5} (5 g) - \frac{1}{5} \cdot 10 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.2.4

Rewrite the expression.

$- 1 g - \frac{1}{5} \cdot 10 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.3

Cancel the common factor of $5$ .

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Step 2.1.3.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$- 1 g + \frac{- 1}{5} \cdot 10 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.3.2

Factor $5$ out of $10$ .

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

Step 2.1.3.3

Cancel the common factor.

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

Step 2.1.3.4

Rewrite the expression.

$- 1 g - 1 \cdot 2 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.4

Multiply $- 1$ by $2$ .

$- 1 g - 2 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.1.5

Rewrite $- 1 g$ as $- g$ .

$- g - 2 - g = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 2.2

Subtract $g$ from $- g$ .

$- 2 g - 2 = 2 - \frac{3}{2} \cdot (4 g - 2)$

Step 3

Simplify $2 - \frac{3}{2} \cdot (4 g - 2)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 2 g - 2 = 2 - \frac{3}{2} (4 g) - \frac{3}{2} \cdot - 2$

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$- 2 g - 2 = 2 + \frac{- 3}{2} (4 g) - \frac{3}{2} \cdot - 2$

Step 3.1.2.2

Factor $2$ out of $4 g$ .

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

Step 3.1.2.3

Cancel the common factor.

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

Step 3.1.2.4

Rewrite the expression.

$- 2 g - 2 = 2 - 3 (2 g) - \frac{3}{2} \cdot - 2$

Step 3.1.3

Multiply $2$ by $- 3$ .

$- 2 g - 2 = 2 - 6 g - \frac{3}{2} \cdot - 2$

Step 3.1.4

Cancel the common factor of $2$ .

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Step 3.1.4.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$- 2 g - 2 = 2 - 6 g + \frac{- 3}{2} \cdot - 2$

Step 3.1.4.2

Factor $2$ out of $- 2$ .

$- 2 g - 2 = 2 - 6 g + \frac{- 3}{2} \cdot (2 (- 1))$

Step 3.1.4.3

Cancel the common factor.

$- 2 g - 2 = 2 - 6 g + \frac{- 3}{2} \cdot (2 \cdot - 1)$

Step 3.1.4.4

Rewrite the expression.

$- 2 g - 2 = 2 - 6 g - 3 \cdot - 1$

Step 3.1.5

Multiply $- 3$ by $- 1$ .

$- 2 g - 2 = 2 - 6 g + 3$

Step 3.2

Add $2$ and $3$ .

$- 2 g - 2 = - 6 g + 5$

Step 4

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

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Step 4.1

Add $6 g$ to both sides of the equation.

$- 2 g - 2 + 6 g = 5$

Step 4.2

Add $- 2 g$ and $6 g$ .

$4 g - 2 = 5$

Step 5

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

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Step 5.1

Add $2$ to both sides of the equation.

$4 g = 5 + 2$

Step 5.2

Add $5$ and $2$ .

$4 g = 7$

Step 6

Divide each term in $4 g = 7$ by $4$ and simplify.

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Step 6.1

Divide each term in $4 g = 7$ by $4$ .

$\frac{4 g}{4} = \frac{7}{4}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{4 g}{4} = \frac{7}{4}$

Step 6.2.1.2

Divide $g$ by $1$ .

$g = \frac{7}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$g = \frac{7}{4}$

Decimal Form:

$g = 1.75$

Mixed Number Form:

$g = 1 \frac{3}{4}$