Basic Math Examples

| 4 y - 3 | = 6

$| 4 y - 3 | = 6$

Step 1

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

4 y - 3 = \pm 6

$4 y - 3 = \pm 6$

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

$\pm$ to find the first solution.

4 y - 3 = 6

$4 y - 3 = 6$

Step 2.2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 2.2.1

Add

3

$3$ to both sides of the equation.

4 y = 6 + 3

$4 y = 6 + 3$

Step 2.2.2

Add

6

$6$ and

3

$3$ .

4 y = 9

$4 y = 9$

4 y = 9

$4 y = 9$

Step 2.3

Divide each term in

4 y = 9

$4 y = 9$ by

4

$4$ and simplify.

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Step 2.3.1

Divide each term in

4 y = 9

$4 y = 9$ by

4

$4$ .

\frac{4 y}{4} = \frac{9}{4}

$\frac{4 y}{4} = \frac{9}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of

4

$4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{9}{4}$

Step 2.3.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{9}{4}$

Step 2.4

Next, use the negative value of the

$\pm$ to find the second solution.

$4 y - 3 = - 6$

Step 2.5

Move all terms not containing

$y$ to the right side of the equation.

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Step 2.5.1

Add

$3$ to both sides of the equation.

$4 y = - 6 + 3$

Step 2.5.2

Add

$- 6$ and

$3$ .

$4 y = - 3$

Step 2.6

Divide each term in

$4 y = - 3$ by

$4$ and simplify.

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Step 2.6.1

Divide each term in

$4 y = - 3$ by

$4$ .

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

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of

$4$ .

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Step 2.6.2.1.1

Cancel the common factor.

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

Step 2.6.2.1.2

Divide

$y$ by

$1$ .

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

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Move the negative in front of the fraction.

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

Step 2.7

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

$y = \frac{9}{4}, - \frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{9}{4}, - \frac{3}{4}$

Decimal Form:

$y = 2.25, - 0.75$

Mixed Number Form:

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