Pre-Algebra Examples

$\frac{2}{11} x - \frac{1}{2} x = \frac{3}{4} x + 1$

Step 1

Simplify $\frac{2}{11} x - \frac{1}{2} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{2}{11}$ and $x$ .

$\frac{2 x}{11} - \frac{1}{2} x = \frac{3}{4} x + 1$

Step 1.1.2

Combine $x$ and $\frac{1}{2}$ .

$\frac{2 x}{11} - \frac{x}{2} = \frac{3}{4} x + 1$

Step 1.2

To write $\frac{2 x}{11}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x}{11} \cdot \frac{2}{2} - \frac{x}{2} = \frac{3}{4} x + 1$

Step 1.3

To write $- \frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{2 x}{11} \cdot \frac{2}{2} - \frac{x}{2} \cdot \frac{11}{11} = \frac{3}{4} x + 1$

Step 1.4

Write each expression with a common denominator of $22$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{2 x}{11}$ by $\frac{2}{2}$ .

$\frac{2 x \cdot 2}{11 \cdot 2} - \frac{x}{2} \cdot \frac{11}{11} = \frac{3}{4} x + 1$

Step 1.4.2

Multiply $11$ by $2$ .

$\frac{2 x \cdot 2}{22} - \frac{x}{2} \cdot \frac{11}{11} = \frac{3}{4} x + 1$

Step 1.4.3

Multiply $\frac{x}{2}$ by $\frac{11}{11}$ .

$\frac{2 x \cdot 2}{22} - \frac{x \cdot 11}{2 \cdot 11} = \frac{3}{4} x + 1$

Step 1.4.4

Multiply $2$ by $11$ .

$\frac{2 x \cdot 2}{22} - \frac{x \cdot 11}{22} = \frac{3}{4} x + 1$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - x \cdot 11}{22} = \frac{3}{4} x + 1$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $x$ out of $2 x \cdot 2 - x \cdot 11$ .

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Step 1.6.1.1

Factor $x$ out of $2 x \cdot 2$ .

$\frac{x (2 \cdot 2) - x \cdot 11}{22} = \frac{3}{4} x + 1$

Step 1.6.1.2

Factor $x$ out of $- x \cdot 11$ .

$\frac{x (2 \cdot 2) + x (- 1 \cdot 11)}{22} = \frac{3}{4} x + 1$

Step 1.6.1.3

Factor $x$ out of $x (2 \cdot 2) + x (- 1 \cdot 11)$ .

$\frac{x (2 \cdot 2 - 1 \cdot 11)}{22} = \frac{3}{4} x + 1$

Step 1.6.2

Multiply $2$ by $2$ .

$\frac{x (4 - 1 \cdot 11)}{22} = \frac{3}{4} x + 1$

Step 1.6.3

Multiply $- 1$ by $11$ .

$\frac{x (4 - 11)}{22} = \frac{3}{4} x + 1$

Step 1.6.4

Subtract $11$ from $4$ .

$\frac{x \cdot - 7}{22} = \frac{3}{4} x + 1$

Step 1.7

Simplify the expression.

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Step 1.7.1

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{22} = \frac{3}{4} x + 1$

Step 1.7.2

Move the negative in front of the fraction.

$- \frac{7 x}{22} = \frac{3}{4} x + 1$

Step 2

Combine $\frac{3}{4}$ and $x$ .

$- \frac{7 x}{22} = \frac{3 x}{4} + 1$

Step 3

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

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Step 3.1

Subtract $\frac{3 x}{4}$ from both sides of the equation.

$- \frac{7 x}{22} - \frac{3 x}{4} = 1$

Step 3.2

To write $- \frac{7 x}{22}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{7 x}{22} \cdot \frac{2}{2} - \frac{3 x}{4} = 1$

Step 3.3

To write $- \frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$- \frac{7 x}{22} \cdot \frac{2}{2} - \frac{3 x}{4} \cdot \frac{11}{11} = 1$

Step 3.4

Write each expression with a common denominator of $44$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{7 x}{22}$ by $\frac{2}{2}$ .

$- \frac{7 x \cdot 2}{22 \cdot 2} - \frac{3 x}{4} \cdot \frac{11}{11} = 1$

Step 3.4.2

Multiply $22$ by $2$ .

$- \frac{7 x \cdot 2}{44} - \frac{3 x}{4} \cdot \frac{11}{11} = 1$

Step 3.4.3

Multiply $\frac{3 x}{4}$ by $\frac{11}{11}$ .

$- \frac{7 x \cdot 2}{44} - \frac{3 x \cdot 11}{4 \cdot 11} = 1$

Step 3.4.4

Multiply $4$ by $11$ .

$- \frac{7 x \cdot 2}{44} - \frac{3 x \cdot 11}{44} = 1$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 7 x \cdot 2 - 3 x \cdot 11}{44} = 1$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Factor $x$ out of $- 7 x \cdot 2 - 3 x \cdot 11$ .

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Step 3.6.1.1

Factor $x$ out of $- 7 x \cdot 2$ .

$\frac{x (- 7 \cdot 2) - 3 x \cdot 11}{44} = 1$

Step 3.6.1.2

Factor $x$ out of $- 3 x \cdot 11$ .

$\frac{x (- 7 \cdot 2) + x (- 3 \cdot 11)}{44} = 1$

Step 3.6.1.3

Factor $x$ out of $x (- 7 \cdot 2) + x (- 3 \cdot 11)$ .

$\frac{x (- 7 \cdot 2 - 3 \cdot 11)}{44} = 1$

Step 3.6.2

Multiply $- 7$ by $2$ .

$\frac{x (- 14 - 3 \cdot 11)}{44} = 1$

Step 3.6.3

Multiply $- 3$ by $11$ .

$\frac{x (- 14 - 33)}{44} = 1$

Step 3.6.4

Subtract $33$ from $- 14$ .

$\frac{x \cdot - 47}{44} = 1$

Step 3.7

Move $- 47$ to the left of $x$ .

$\frac{- 47 \cdot x}{44} = 1$

Step 3.8

Move the negative in front of the fraction.

$- \frac{47 x}{44} = 1$

Step 4

Multiply both sides of the equation by $- \frac{44}{47}$ .

$- \frac{44}{47} (- \frac{47 x}{44}) = - \frac{44}{47} \cdot 1$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{44}{47} (- \frac{47 x}{44})$ .

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Step 5.1.1.1

Cancel the common factor of $44$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{44}{47}$ into the numerator.

$\frac{- 44}{47} (- \frac{47 x}{44}) = - \frac{44}{47} \cdot 1$

Step 5.1.1.1.2

Move the leading negative in $- \frac{47 x}{44}$ into the numerator.

$\frac{- 44}{47} \cdot \frac{- 47 x}{44} = - \frac{44}{47} \cdot 1$

Step 5.1.1.1.3

Factor $44$ out of $- 44$ .

$\frac{44 (- 1)}{47} \cdot \frac{- 47 x}{44} = - \frac{44}{47} \cdot 1$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{44 \cdot - 1}{47} \cdot \frac{- 47 x}{44} = - \frac{44}{47} \cdot 1$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{47} (- 47 x) = - \frac{44}{47} \cdot 1$

Step 5.1.1.2

Cancel the common factor of $47$ .

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Step 5.1.1.2.1

Factor $47$ out of $- 47 x$ .

$\frac{- 1}{47} (47 (- x)) = - \frac{44}{47} \cdot 1$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{47} (47 (- x)) = - \frac{44}{47} \cdot 1$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{44}{47} \cdot 1$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{44}{47} \cdot 1$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{44}{47} \cdot 1$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 1$ by $1$ .

$x = - \frac{44}{47}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{44}{47}$

Decimal Form:

$x = - 0.93617021 \dots$