Basic Math Examples

$| \frac{3}{2 y - 1} | = 4$

Step 1

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

$\frac{3}{2 y - 1} = \pm 4$

Step 2

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

Tap for more steps...

Step 2.1

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

$\frac{3}{2 y - 1} = 4$

Step 2.2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 y - 1, 1$

Step 2.2.2

Remove parentheses.

$2 y - 1, 1$

Step 2.2.3

The LCM of one and any expression is the expression.

$2 y - 1$

Step 2.3

Multiply each term in $\frac{3}{2 y - 1} = 4$ by $2 y - 1$ to eliminate the fractions.

Tap for more steps...

Step 2.3.1

Multiply each term in $\frac{3}{2 y - 1} = 4$ by $2 y - 1$ .

$\frac{3}{2 y - 1} (2 y - 1) = 4 (2 y - 1)$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $2 y - 1$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{3}{2 y - 1} (2 y - 1) = 4 (2 y - 1)$

Step 2.3.2.1.2

Rewrite the expression.

$3 = 4 (2 y - 1)$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Apply the distributive property.

$3 = 4 (2 y) + 4 \cdot - 1$

Step 2.3.3.2

Multiply.

Tap for more steps...

Step 2.3.3.2.1

Multiply $2$ by $4$ .

$3 = 8 y + 4 \cdot - 1$

Step 2.3.3.2.2

Multiply $4$ by $- 1$ .

$3 = 8 y - 4$

Step 2.4

Solve the equation.

Tap for more steps...

Step 2.4.1

Rewrite the equation as $8 y - 4 = 3$ .

$8 y - 4 = 3$

Step 2.4.2

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

Tap for more steps...

Step 2.4.2.1

Add $4$ to both sides of the equation.

$8 y = 3 + 4$

Step 2.4.2.2

Add $3$ and $4$ .

$8 y = 7$

Step 2.4.3

Divide each term in $8 y = 7$ by $8$ and simplify.

Tap for more steps...

Step 2.4.3.1

Divide each term in $8 y = 7$ by $8$ .

$\frac{8 y}{8} = \frac{7}{8}$

Step 2.4.3.2

Simplify the left side.

Tap for more steps...

Step 2.4.3.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.4.3.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{7}{8}$

Step 2.4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{8}$

Step 2.5

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

$\frac{3}{2 y - 1} = - 4$

Step 2.6

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.6.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 y - 1, 1$

Step 2.6.2

Remove parentheses.

$2 y - 1, 1$

Step 2.6.3

The LCM of one and any expression is the expression.

$2 y - 1$

Step 2.7

Multiply each term in $\frac{3}{2 y - 1} = - 4$ by $2 y - 1$ to eliminate the fractions.

Tap for more steps...

Step 2.7.1

Multiply each term in $\frac{3}{2 y - 1} = - 4$ by $2 y - 1$ .

$\frac{3}{2 y - 1} (2 y - 1) = - 4 (2 y - 1)$

Step 2.7.2

Simplify the left side.

Tap for more steps...

Step 2.7.2.1

Cancel the common factor of $2 y - 1$ .

Tap for more steps...

Step 2.7.2.1.1

Cancel the common factor.

$\frac{3}{2 y - 1} (2 y - 1) = - 4 (2 y - 1)$

Step 2.7.2.1.2

Rewrite the expression.

$3 = - 4 (2 y - 1)$

Step 2.7.3

Simplify the right side.

Tap for more steps...

Step 2.7.3.1

Apply the distributive property.

$3 = - 4 (2 y) - 4 \cdot - 1$

Step 2.7.3.2

Multiply.

Tap for more steps...

Step 2.7.3.2.1

Multiply $2$ by $- 4$ .

$3 = - 8 y - 4 \cdot - 1$

Step 2.7.3.2.2

Multiply $- 4$ by $- 1$ .

$3 = - 8 y + 4$

Step 2.8

Solve the equation.

Tap for more steps...

Step 2.8.1

Rewrite the equation as $- 8 y + 4 = 3$ .

$- 8 y + 4 = 3$

Step 2.8.2

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

Tap for more steps...

Step 2.8.2.1

Subtract $4$ from both sides of the equation.

$- 8 y = 3 - 4$

Step 2.8.2.2

Subtract $4$ from $3$ .

$- 8 y = - 1$

Step 2.8.3

Divide each term in $- 8 y = - 1$ by $- 8$ and simplify.

Tap for more steps...

Step 2.8.3.1

Divide each term in $- 8 y = - 1$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 1}{- 8}$

Step 2.8.3.2

Simplify the left side.

Tap for more steps...

Step 2.8.3.2.1

Cancel the common factor of $- 8$ .

Tap for more steps...

Step 2.8.3.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 1}{- 8}$

Step 2.8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 1}{- 8}$

Step 2.8.3.3

Simplify the right side.

Tap for more steps...

Step 2.8.3.3.1

Dividing two negative values results in a positive value.

$y = \frac{1}{8}$

Step 2.9

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

$y = \frac{7}{8}, \frac{1}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{8}, \frac{1}{8}$

Decimal Form:

$y = 0.875, 0.125$