Finite Math Examples

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

$3 g + 5 = (4 - g) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(4 - g) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$3 g + 5 = 4 \cdot 2 - g \cdot 2$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Multiply $4$ by $2$ .

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

Step 2.2.1.2.2

Multiply $2$ by $- 1$ .

$3 g + 5 = 8 - 2 g$

Step 2.2.1.2.3

Reorder $8$ and $- 2 g$ .

$3 g + 5 = - 2 g + 8$

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

Add $2 g$ to both sides of the equation.

$3 g + 5 + 2 g = 8$

Step 3.1.2

Add $3 g$ and $2 g$ .

$5 g + 5 = 8$

Step 3.2

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

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Step 3.2.1

Subtract $5$ from both sides of the equation.

$5 g = 8 - 5$

Step 3.2.2

Subtract $5$ from $8$ .

$5 g = 3$

Step 3.3

Divide each term in $5 g = 3$ by $5$ and simplify.

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Step 3.3.1

Divide each term in $5 g = 3$ by $5$ .

$\frac{5 g}{5} = \frac{3}{5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{5 g}{5} = \frac{3}{5}$

Step 3.3.2.1.2

Divide $g$ by $1$ .

$g = \frac{3}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$g = \frac{3}{5}$

Decimal Form:

$g = 0.6$