Basic Math Examples

$| 5 y - 1 | = 5 y$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$5 y - 1 = \pm 5 y$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$5 y - 1 = 5 y$

Step 2.2

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

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Step 2.2.1

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

$5 y - 1 - 5 y = 0$

Step 2.2.2

Combine the opposite terms in $5 y - 1 - 5 y$ .

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Step 2.2.2.1

Subtract $5 y$ from $5 y$ .

$0 - 1 = 0$

Step 2.2.2.2

Subtract $1$ from $0$ .

$- 1 = 0$

Step 2.3

Since $- 1 \neq 0$ , there are no solutions.

No solution

Step 2.4

Next, use the negative value of the $\pm$ to find the second solution.

$5 y - 1 = - 5 y$

Step 2.5

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

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Step 2.5.1

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

$5 y - 1 + 5 y = 0$

Step 2.5.2

Add $5 y$ and $5 y$ .

$10 y - 1 = 0$

Step 2.6

Add $1$ to both sides of the equation.

$10 y = 1$

Step 2.7

Divide each term in $10 y = 1$ by $10$ and simplify.

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Step 2.7.1

Divide each term in $10 y = 1$ by $10$ .

$\frac{10 y}{10} = \frac{1}{10}$

Step 2.7.2

Simplify the left side.

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Step 2.7.2.1

Cancel the common factor of $10$ .

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Step 2.7.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{1}{10}$

Step 2.7.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{10}$

Step 2.8

The complete solution is the result of both the positive and negative portions of the solution.

$y =$