Pre-Algebra Examples

$5 - \frac{2 x - 1}{4} = \frac{x + 2}{3}$

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(5 - \frac{2 x - 1}{4}) \cdot 3$ .

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Step 2.1.1.1

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

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

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

Combine $5$ and $\frac{4}{4}$ .

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

Step 2.1.1.2.2

Combine the numerators over the common denominator.

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

Step 2.1.1.3

Simplify the numerator.

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Step 2.1.1.3.1

Multiply $5$ by $4$ .

$\frac{20 - (2 x - 1)}{4} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Step 2.1.1.3.2

Apply the distributive property.

$\frac{20 - (2 x) - - 1}{4} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Step 2.1.1.3.3

Multiply $2$ by $- 1$ .

$\frac{20 - 2 x - - 1}{4} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Step 2.1.1.3.4

Multiply $- 1$ by $- 1$ .

$\frac{20 - 2 x + 1}{4} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Step 2.1.1.3.5

Add $20$ and $1$ .

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

Step 2.1.1.4

Simplify terms.

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Step 2.1.1.4.1

Combine $\frac{- 2 x + 21}{4}$ and $3$ .

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

Step 2.1.1.4.2

Move $3$ to the left of $- 2 x + 21$ .

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

Step 2.1.1.4.3

Factor $- 1$ out of $- 2 x$ .

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

Step 2.1.1.4.4

Rewrite $21$ as $- 1 (- 21)$ .

$\frac{3 (- (2 x) - 1 (- 21))}{4} = \frac{x + 2}{3} \cdot 3$

Step 2.1.1.4.5

Factor $- 1$ out of $- (2 x) - 1 (- 21)$ .

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

Step 2.1.1.4.6

Simplify the expression.

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Step 2.1.1.4.6.1

Rewrite $- (2 x - 21)$ as $- 1 (2 x - 21)$ .

$\frac{3 (- 1 (2 x - 21))}{4} = \frac{x + 2}{3} \cdot 3$

Step 2.1.1.4.6.2

Move the negative in front of the fraction.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$- \frac{3 (2 x - 21)}{4} = x + 2$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $4$ .

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

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 $- \frac{3 (2 x - 21)}{4} \cdot 4$ .

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Step 3.2.1.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1.1

Move the leading negative in $- \frac{3 (2 x - 21)}{4}$ into the numerator.

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

Step 3.2.1.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.1.3

Rewrite the expression.

$- 3 (2 x - 21) = (x + 2) \cdot 4$

Step 3.2.1.1.2

Apply the distributive property.

$- 3 (2 x) - 3 \cdot - 21 = (x + 2) \cdot 4$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $2$ by $- 3$ .

$- 6 x - 3 \cdot - 21 = (x + 2) \cdot 4$

Step 3.2.1.1.3.2

Multiply $- 3$ by $- 21$ .

$- 6 x + 63 = (x + 2) \cdot 4$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(x + 2) \cdot 4$ .

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Step 3.2.2.1.1

Apply the distributive property.

$- 6 x + 63 = x \cdot 4 + 2 \cdot 4$

Step 3.2.2.1.2

Simplify the expression.

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Step 3.2.2.1.2.1

Move $4$ to the left of $x$ .

$- 6 x + 63 = 4 \cdot x + 2 \cdot 4$

Step 3.2.2.1.2.2

Multiply $2$ by $4$ .

$- 6 x + 63 = 4 x + 8$

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 $4 x$ from both sides of the equation.

$- 6 x + 63 - 4 x = 8$

Step 3.3.1.2

Subtract $4 x$ from $- 6 x$ .

$- 10 x + 63 = 8$

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

Subtract $63$ from both sides of the equation.

$- 10 x = 8 - 63$

Step 3.3.2.2

Subtract $63$ from $8$ .

$- 10 x = - 55$

Step 3.3.3

Divide each term in $- 10 x = - 55$ by $- 10$ and simplify.

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Step 3.3.3.1

Divide each term in $- 10 x = - 55$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 55}{- 10}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 10$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 55}{- 10}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 55}{- 10}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Cancel the common factor of $- 55$ and $- 10$ .

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Step 3.3.3.3.1.1

Factor $- 5$ out of $- 55$ .

$x = \frac{- 5 (11)}{- 10}$

Step 3.3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.3.1.2.1

Factor $- 5$ out of $- 10$ .

$x = \frac{- 5 \cdot 11}{- 5 \cdot 2}$

Step 3.3.3.3.1.2.2

Cancel the common factor.

$x = \frac{- 5 \cdot 11}{- 5 \cdot 2}$

Step 3.3.3.3.1.2.3

Rewrite the expression.

$x = \frac{11}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{2}$

Decimal Form:

$x = 5.5$

Mixed Number Form:

$x = 5 \frac{1}{2}$