Basic Math Examples

$- 7 = \frac{5 u - 2}{- 4}$

Step 1

Rewrite the equation as $\frac{5 u - 2}{- 4} = - 7$ .

$\frac{5 u - 2}{- 4} = - 7$

Step 2

Multiply both sides by $- 4$ .

$\frac{5 u - 2}{- 4} \cdot - 4 = - 7 \cdot - 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{5 u - 2}{- 4} \cdot - 4$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Factor $4$ out of $- 4$ .

$\frac{5 u - 2}{4 (- 1)} \cdot - 4 = - 7 \cdot - 4$

Step 3.1.1.1.2

Factor $4$ out of $- 4$ .

$\frac{5 u - 2}{4 \cdot - 1} \cdot (4 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.1.3

Cancel the common factor.

$\frac{5 u - 2}{4 \cdot - 1} \cdot (4 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.1.4

Rewrite the expression.

$\frac{5 u - 2}{- 1} \cdot - 1 = - 7 \cdot - 4$

Step 3.1.1.2

Combine $\frac{5 u - 2}{- 1}$ and $- 1$ .

$\frac{(5 u - 2) \cdot - 1}{- 1} = - 7 \cdot - 4$

Step 3.1.1.3

Simplify the expression.

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Step 3.1.1.3.1

Move the negative one from the denominator of $\frac{(5 u - 2) \cdot - 1}{- 1}$ .

$- 1 \cdot ((5 u - 2) \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.3.2

Rewrite $- 1 \cdot ((5 u - 2) \cdot - 1)$ as $- ((5 u - 2) \cdot - 1)$ .

$- ((5 u - 2) \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.4

Apply the distributive property.

$- (5 u \cdot - 1 - 2 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.5

Multiply.

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Step 3.1.1.5.1

Multiply $- 1$ by $5$ .

$- (- 5 u - 2 \cdot - 1) = - 7 \cdot - 4$

Step 3.1.1.5.2

Multiply $- 2$ by $- 1$ .

$- (- 5 u + 2) = - 7 \cdot - 4$

Step 3.1.1.6

Apply the distributive property.

$- (- 5 u) - 1 \cdot 2 = - 7 \cdot - 4$

Step 3.1.1.7

Multiply.

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Step 3.1.1.7.1

Multiply $- 5$ by $- 1$ .

$5 u - 1 \cdot 2 = - 7 \cdot - 4$

Step 3.1.1.7.2

Multiply $- 1$ by $2$ .

$5 u - 2 = - 7 \cdot - 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 7$ by $- 4$ .

$5 u - 2 = 28$

Step 4

Solve for $u$ .

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Step 4.1

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

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Step 4.1.1

Add $2$ to both sides of the equation.

$5 u = 28 + 2$

Step 4.1.2

Add $28$ and $2$ .

$5 u = 30$

Step 4.2

Divide each term in $5 u = 30$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 u = 30$ by $5$ .

$\frac{5 u}{5} = \frac{30}{5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 u}{5} = \frac{30}{5}$

Step 4.2.2.1.2

Divide $u$ by $1$ .

$u = \frac{30}{5}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $30$ by $5$ .

$u = 6$