Basic Math Examples

$4 = \frac{3 u - 4}{4} + \frac{u - 9}{8}$

Step 1

Rewrite the equation as $\frac{3 u - 4}{4} + \frac{u - 9}{8} = 4$ .

$\frac{3 u - 4}{4} + \frac{u - 9}{8} = 4$

Step 2

Simplify $\frac{3 u - 4}{4} + \frac{u - 9}{8}$ .

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Step 2.1

To write $\frac{3 u - 4}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 u - 4}{4} \cdot \frac{2}{2} + \frac{u - 9}{8} = 4$

Step 2.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{3 u - 4}{4}$ by $\frac{2}{2}$ .

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

Step 2.2.2

Multiply $4$ by $2$ .

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Simplify the numerator.

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Step 2.4.1

Apply the distributive property.

$\frac{3 u \cdot 2 - 4 \cdot 2 + u - 9}{8} = 4$

Step 2.4.2

Multiply $2$ by $3$ .

$\frac{6 u - 4 \cdot 2 + u - 9}{8} = 4$

Step 2.4.3

Multiply $- 4$ by $2$ .

$\frac{6 u - 8 + u - 9}{8} = 4$

Step 2.4.4

Add $6 u$ and $u$ .

$\frac{7 u - 8 - 9}{8} = 4$

Step 2.4.5

Subtract $9$ from $- 8$ .

$\frac{7 u - 17}{8} = 4$

Step 3

Multiply both sides by $8$ .

$\frac{7 u - 17}{8} \cdot 8 = 4 \cdot 8$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{7 u - 17}{8} \cdot 8 = 4 \cdot 8$

Step 4.1.1.2

Rewrite the expression.

$7 u - 17 = 4 \cdot 8$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $8$ .

$7 u - 17 = 32$

Step 5

Solve for $u$ .

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Step 5.1

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

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Step 5.1.1

Add $17$ to both sides of the equation.

$7 u = 32 + 17$

Step 5.1.2

Add $32$ and $17$ .

$7 u = 49$

Step 5.2

Divide each term in $7 u = 49$ by $7$ and simplify.

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Step 5.2.1

Divide each term in $7 u = 49$ by $7$ .

$\frac{7 u}{7} = \frac{49}{7}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $7$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{7 u}{7} = \frac{49}{7}$

Step 5.2.2.1.2

Divide $u$ by $1$ .

$u = \frac{49}{7}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $49$ by $7$ .

$u = 7$