Pre-Algebra Examples

$\frac{2 x - 1}{15} - \frac{4 - x}{18} = \frac{3 x - 10}{12}$

Step 1

Multiply both sides by $12$ .

$(\frac{2 x - 1}{15} - \frac{4 - x}{18}) \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{2 x - 1}{15} - \frac{4 - x}{18}) \cdot 12$ .

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Step 2.1.1.1

To write $\frac{2 x - 1}{15}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(\frac{2 x - 1}{15} \cdot \frac{6}{6} - \frac{4 - x}{18}) \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.2

To write $- \frac{4 - x}{18}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{2 x - 1}{15} \cdot \frac{6}{6} - \frac{4 - x}{18} \cdot \frac{5}{5}) \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.3

Write each expression with a common denominator of $90$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.3.1

Multiply $\frac{2 x - 1}{15}$ by $\frac{6}{6}$ .

$(\frac{(2 x - 1) \cdot 6}{15 \cdot 6} - \frac{4 - x}{18} \cdot \frac{5}{5}) \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.3.2

Multiply $15$ by $6$ .

$(\frac{(2 x - 1) \cdot 6}{90} - \frac{4 - x}{18} \cdot \frac{5}{5}) \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.3.3

Multiply $\frac{4 - x}{18}$ by $\frac{5}{5}$ .

$(\frac{(2 x - 1) \cdot 6}{90} - \frac{(4 - x) \cdot 5}{18 \cdot 5}) \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.3.4

Multiply $18$ by $5$ .

$(\frac{(2 x - 1) \cdot 6}{90} - \frac{(4 - x) \cdot 5}{90}) \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{(2 x - 1) \cdot 6 - (4 - x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Apply the distributive property.

$\frac{2 x \cdot 6 - 1 \cdot 6 - (4 - x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.2

Multiply $6$ by $2$ .

$\frac{12 x - 1 \cdot 6 - (4 - x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.3

Multiply $- 1$ by $6$ .

$\frac{12 x - 6 - (4 - x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.4

Apply the distributive property.

$\frac{12 x - 6 + (- 1 \cdot 4 - - x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.5

Multiply $- 1$ by $4$ .

$\frac{12 x - 6 + (- 4 - - x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.6

Multiply $- - x$ .

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Step 2.1.1.5.6.1

Multiply $- 1$ by $- 1$ .

$\frac{12 x - 6 + (- 4 + 1 x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.6.2

Multiply $x$ by $1$ .

$\frac{12 x - 6 + (- 4 + x) \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.7

Apply the distributive property.

$\frac{12 x - 6 - 4 \cdot 5 + x \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.8

Multiply $- 4$ by $5$ .

$\frac{12 x - 6 - 20 + x \cdot 5}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.9

Move $5$ to the left of $x$ .

$\frac{12 x - 6 - 20 + 5 \cdot x}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.10

Add $12 x$ and $5 x$ .

$\frac{17 x - 6 - 20}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.5.11

Subtract $20$ from $- 6$ .

$\frac{17 x - 26}{90} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.6

Simplify terms.

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Step 2.1.1.6.1

Cancel the common factor of $6$ .

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Step 2.1.1.6.1.1

Factor $6$ out of $90$ .

$\frac{17 x - 26}{6 (15)} \cdot 12 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.6.1.2

Factor $6$ out of $12$ .

$\frac{17 x - 26}{6 \cdot 15} \cdot (6 \cdot 2) = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.6.1.3

Cancel the common factor.

$\frac{17 x - 26}{6 \cdot 15} \cdot (6 \cdot 2) = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.6.1.4

Rewrite the expression.

$\frac{17 x - 26}{15} \cdot 2 = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.6.2

Combine $\frac{17 x - 26}{15}$ and $2$ .

$\frac{(17 x - 26) \cdot 2}{15} = \frac{3 x - 10}{12} \cdot 12$

Step 2.1.1.6.3

Move $2$ to the left of $17 x - 26$ .

$\frac{2 (17 x - 26)}{15} = \frac{3 x - 10}{12} \cdot 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 (17 x - 26)}{15} = \frac{3 x - 10}{12} \cdot 12$

Step 2.2.1.2

Rewrite the expression.

$\frac{2 (17 x - 26)}{15} = 3 x - 10$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $15$ .

$\frac{2 (17 x - 26)}{15} \cdot 15 = (3 x - 10) \cdot 15$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{2 (17 x - 26)}{15} \cdot 15$ .

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Step 3.2.1.1.1

Cancel the common factor of $15$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{2 (17 x - 26)}{15} \cdot 15 = (3 x - 10) \cdot 15$

Step 3.2.1.1.1.2

Rewrite the expression.

$2 (17 x - 26) = (3 x - 10) \cdot 15$

Step 3.2.1.1.2

Apply the distributive property.

$2 (17 x) + 2 \cdot - 26 = (3 x - 10) \cdot 15$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $17$ by $2$ .

$34 x + 2 \cdot - 26 = (3 x - 10) \cdot 15$

Step 3.2.1.1.3.2

Multiply $2$ by $- 26$ .

$34 x - 52 = (3 x - 10) \cdot 15$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(3 x - 10) \cdot 15$ .

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Step 3.2.2.1.1

Apply the distributive property.

$34 x - 52 = 3 x \cdot 15 - 10 \cdot 15$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $15$ by $3$ .

$34 x - 52 = 45 x - 10 \cdot 15$

Step 3.2.2.1.2.2

Multiply $- 10$ by $15$ .

$34 x - 52 = 45 x - 150$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $45 x$ from both sides of the equation.

$34 x - 52 - 45 x = - 150$

Step 3.3.1.2

Subtract $45 x$ from $34 x$ .

$- 11 x - 52 = - 150$

Step 3.3.2

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

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Step 3.3.2.1

Add $52$ to both sides of the equation.

$- 11 x = - 150 + 52$

Step 3.3.2.2

Add $- 150$ and $52$ .

$- 11 x = - 98$

Step 3.3.3

Divide each term in $- 11 x = - 98$ by $- 11$ and simplify.

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Step 3.3.3.1

Divide each term in $- 11 x = - 98$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 98}{- 11}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 11$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 98}{- 11}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 98}{- 11}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{98}{11}$