Precalculus Examples

$| 5 u + 7 | = | 5 u + 8 |$

Step 1

Rewrite the equation as $| 5 u + 8 | = | 5 u + 7 |$ .

$| 5 u + 8 | = | 5 u + 7 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$5 u + 8 = 5 u + 7$

$5 u + 8 = - (5 u + 7)$

$- (5 u + 8) = 5 u + 7$

$- (5 u + 8) = - (5 u + 7)$

Step 3

After simplifying, there are only two unique equations to be solved.

$5 u + 8 = 5 u + 7$

$5 u + 8 = - (5 u + 7)$

Step 4

Solve $5 u + 8 = 5 u + 7$ for $u$ .

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Step 4.1

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

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Step 4.1.1

Subtract $5 u$ from both sides of the equation.

$5 u + 8 - 5 u = 7$

Step 4.1.2

Combine the opposite terms in $5 u + 8 - 5 u$ .

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Step 4.1.2.1

Subtract $5 u$ from $5 u$ .

$0 + 8 = 7$

Step 4.1.2.2

Add $0$ and $8$ .

$8 = 7$

Step 4.2

Since $8 \neq 7$ , there are no solutions.

No solution

Step 5

Solve $5 u + 8 = - (5 u + 7)$ for $u$ .

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Step 5.1

Simplify $- (5 u + 7)$ .

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Step 5.1.1

Rewrite.

$5 u + 8 = 0 + 0 - (5 u + 7)$

Step 5.1.2

Simplify by adding zeros.

$5 u + 8 = - (5 u + 7)$

Step 5.1.3

Apply the distributive property.

$5 u + 8 = - (5 u) - 1 \cdot 7$

Step 5.1.4

Multiply.

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Step 5.1.4.1

Multiply $5$ by $- 1$ .

$5 u + 8 = - 5 u - 1 \cdot 7$

Step 5.1.4.2

Multiply $- 1$ by $7$ .

$5 u + 8 = - 5 u - 7$

Step 5.2

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

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Step 5.2.1

Add $5 u$ to both sides of the equation.

$5 u + 8 + 5 u = - 7$

Step 5.2.2

Add $5 u$ and $5 u$ .

$10 u + 8 = - 7$

Step 5.3

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

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Step 5.3.1

Subtract $8$ from both sides of the equation.

$10 u = - 7 - 8$

Step 5.3.2

Subtract $8$ from $- 7$ .

$10 u = - 15$

Step 5.4

Divide each term in $10 u = - 15$ by $10$ and simplify.

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Step 5.4.1

Divide each term in $10 u = - 15$ by $10$ .

$\frac{10 u}{10} = \frac{- 15}{10}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $10$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{10 u}{10} = \frac{- 15}{10}$

Step 5.4.2.1.2

Divide $u$ by $1$ .

$u = \frac{- 15}{10}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Cancel the common factor of $- 15$ and $10$ .

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Step 5.4.3.1.1

Factor $5$ out of $- 15$ .

$u = \frac{5 (- 3)}{10}$

Step 5.4.3.1.2

Cancel the common factors.

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Step 5.4.3.1.2.1

Factor $5$ out of $10$ .

$u = \frac{5 \cdot - 3}{5 \cdot 2}$

Step 5.4.3.1.2.2

Cancel the common factor.

$u = \frac{5 \cdot - 3}{5 \cdot 2}$

Step 5.4.3.1.2.3

Rewrite the expression.

$u = \frac{- 3}{2}$

Step 5.4.3.2

Move the negative in front of the fraction.

$u = - \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$u = - \frac{3}{2}$

Decimal Form:

$u = - 1.5$

Mixed Number Form:

$u = - 1 \frac{1}{2}$