Algebra Examples

$\frac{21 - 4 x}{9} + \frac{8 x + 15}{3} = 2$

Step 1

Simplify $\frac{21 - 4 x}{9} + \frac{8 x + 15}{3}$ .

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Step 1.1

To write $\frac{8 x + 15}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{21 - 4 x}{9} + \frac{8 x + 15}{3} \cdot \frac{3}{3} = 2$

Step 1.2

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{8 x + 15}{3}$ by $\frac{3}{3}$ .

$\frac{21 - 4 x}{9} + \frac{(8 x + 15) \cdot 3}{3 \cdot 3} = 2$

Step 1.2.2

Multiply $3$ by $3$ .

$\frac{21 - 4 x}{9} + \frac{(8 x + 15) \cdot 3}{9} = 2$

Step 1.3

Combine the numerators over the common denominator.

$\frac{21 - 4 x + (8 x + 15) \cdot 3}{9} = 2$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

$\frac{21 - 4 x + 8 x \cdot 3 + 15 \cdot 3}{9} = 2$

Step 1.4.2

Multiply $3$ by $8$ .

$\frac{21 - 4 x + 24 x + 15 \cdot 3}{9} = 2$

Step 1.4.3

Multiply $15$ by $3$ .

$\frac{21 - 4 x + 24 x + 45}{9} = 2$

Step 1.4.4

Add $21$ and $45$ .

$\frac{- 4 x + 24 x + 66}{9} = 2$

Step 1.4.5

Add $- 4 x$ and $24 x$ .

$\frac{20 x + 66}{9} = 2$

Step 1.4.6

Factor $2$ out of $20 x + 66$ .

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Step 1.4.6.1

Factor $2$ out of $20 x$ .

$\frac{2 (10 x) + 66}{9} = 2$

Step 1.4.6.2

Factor $2$ out of $66$ .

$\frac{2 (10 x) + 2 (33)}{9} = 2$

Step 1.4.6.3

Factor $2$ out of $2 (10 x) + 2 (33)$ .

$\frac{2 (10 x + 33)}{9} = 2$

Step 2

Multiply both sides by $9$ .

$\frac{2 (10 x + 33)}{9} \cdot 9 = 2 \cdot 9$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2 (10 x + 33)}{9} \cdot 9$ .

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Step 3.1.1.1

Cancel the common factor of $9$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2 (10 x + 33)}{9} \cdot 9 = 2 \cdot 9$

Step 3.1.1.1.2

Rewrite the expression.

$2 (10 x + 33) = 2 \cdot 9$

Step 3.1.1.2

Apply the distributive property.

$2 (10 x) + 2 \cdot 33 = 2 \cdot 9$

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $10$ by $2$ .

$20 x + 2 \cdot 33 = 2 \cdot 9$

Step 3.1.1.3.2

Multiply $2$ by $33$ .

$20 x + 66 = 2 \cdot 9$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $9$ .

$20 x + 66 = 18$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $66$ from both sides of the equation.

$20 x = 18 - 66$

Step 4.1.2

Subtract $66$ from $18$ .

$20 x = - 48$

Step 4.2

Divide each term in $20 x = - 48$ by $20$ and simplify.

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Step 4.2.1

Divide each term in $20 x = - 48$ by $20$ .

$\frac{20 x}{20} = \frac{- 48}{20}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $20$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{20 x}{20} = \frac{- 48}{20}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 48}{20}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $- 48$ and $20$ .

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Step 4.2.3.1.1

Factor $4$ out of $- 48$ .

$x = \frac{4 (- 12)}{20}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $4$ out of $20$ .

$x = \frac{4 \cdot - 12}{4 \cdot 5}$

Step 4.2.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot - 12}{4 \cdot 5}$

Step 4.2.3.1.2.3

Rewrite the expression.

$x = \frac{- 12}{5}$

Step 4.2.3.2

Move the negative in front of the fraction.

$x = - \frac{12}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{12}{5}$

Decimal Form:

$x = - 2.4$

Mixed Number Form:

$x = - 2 \frac{2}{5}$