Basic Math Examples

$| 5 v - 7 | = | 5 v - 8 |$

Step 1

Rewrite the equation as $| 5 v - 8 | = | 5 v - 7 |$ .

$| 5 v - 8 | = | 5 v - 7 |$

Step 2

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

$5 v - 8 = 5 v - 7$

$5 v - 8 = - (5 v - 7)$

$- (5 v - 8) = 5 v - 7$

$- (5 v - 8) = - (5 v - 7)$

Step 3

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

$5 v - 8 = 5 v - 7$

$5 v - 8 = - (5 v - 7)$

Step 4

Solve $5 v - 8 = 5 v - 7$ for $v$ .

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Step 4.1

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

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Step 4.1.1

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

$5 v - 8 - 5 v = - 7$

Step 4.1.2

Combine the opposite terms in $5 v - 8 - 5 v$ .

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Step 4.1.2.1

Subtract $5 v$ from $5 v$ .

$0 - 8 = - 7$

Step 4.1.2.2

Subtract $8$ from $0$ .

$- 8 = - 7$

Step 4.2

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

No solution

Step 5

Solve $5 v - 8 = - (5 v - 7)$ for $v$ .

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Step 5.1

Simplify $- (5 v - 7)$ .

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Step 5.1.1

Rewrite.

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

Step 5.1.2

Simplify by adding zeros.

$5 v - 8 = - (5 v - 7)$

Step 5.1.3

Apply the distributive property.

$5 v - 8 = - (5 v) - - 7$

Step 5.1.4

Multiply.

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Step 5.1.4.1

Multiply $5$ by $- 1$ .

$5 v - 8 = - 5 v - - 7$

Step 5.1.4.2

Multiply $- 1$ by $- 7$ .

$5 v - 8 = - 5 v + 7$

Step 5.2

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

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Step 5.2.1

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

$5 v - 8 + 5 v = 7$

Step 5.2.2

Add $5 v$ and $5 v$ .

$10 v - 8 = 7$

Step 5.3

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

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Step 5.3.1

Add $8$ to both sides of the equation.

$10 v = 7 + 8$

Step 5.3.2

Add $7$ and $8$ .

$10 v = 15$

Step 5.4

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

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Step 5.4.1

Divide each term in $10 v = 15$ by $10$ .

$\frac{10 v}{10} = \frac{15}{10}$

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.

$\frac{10 v}{10} = \frac{15}{10}$

Step 5.4.2.1.2

Divide $v$ by $1$ .

$v = \frac{15}{10}$

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 $15$ .

$v = \frac{5 (3)}{10}$

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 $10$ .

$v = \frac{5 \cdot 3}{5 \cdot 2}$

Step 5.4.3.1.2.2

Cancel the common factor.

$v = \frac{5 \cdot 3}{5 \cdot 2}$

Step 5.4.3.1.2.3

Rewrite the expression.

$v = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$v = \frac{3}{2}$

Decimal Form:

$v = 1.5$

Mixed Number Form:

$v = 1 \frac{1}{2}$