Basic Math Examples

| 3 s + 5 | = | s - 1 |

$| 3 s + 5 | = | s - 1 |$

Step 1

Rewrite the equation as

| s - 1 | = | 3 s + 5 |

$| s - 1 | = | 3 s + 5 |$ .

| s - 1 | = | 3 s + 5 |

$| s - 1 | = | 3 s + 5 |$

Step 2

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

s - 1 = 3 s + 5

$s - 1 = 3 s + 5$

s - 1 = - (3 s + 5)

$s - 1 = - (3 s + 5)$

- (s - 1) = 3 s + 5

$- (s - 1) = 3 s + 5$

- (s - 1) = - (3 s + 5)

$- (s - 1) = - (3 s + 5)$

Step 3

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

s - 1 = 3 s + 5

$s - 1 = 3 s + 5$

s - 1 = - (3 s + 5)

$s - 1 = - (3 s + 5)$

Step 4

Solve

s - 1 = 3 s + 5

$s - 1 = 3 s + 5$ for

s

$s$ .

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Step 4.1

Move all terms containing

s

$s$ to the left side of the equation.

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Step 4.1.1

Subtract

3 s

$3 s$ from both sides of the equation.

s - 1 - 3 s = 5

$s - 1 - 3 s = 5$

Step 4.1.2

Subtract

3 s

$3 s$ from

s

$s$ .

- 2 s - 1 = 5

$- 2 s - 1 = 5$

- 2 s - 1 = 5

$- 2 s - 1 = 5$

Step 4.2

Move all terms not containing

s

$s$ to the right side of the equation.

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Step 4.2.1

Add

1

$1$ to both sides of the equation.

- 2 s = 5 + 1

$- 2 s = 5 + 1$

Step 4.2.2

Add

5

$5$ and

1

$1$ .

- 2 s = 6

$- 2 s = 6$

- 2 s = 6

$- 2 s = 6$

Step 4.3

Divide each term in

- 2 s = 6

$- 2 s = 6$ by

- 2

$- 2$ and simplify.

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Step 4.3.1

Divide each term in

- 2 s = 6

$- 2 s = 6$ by

- 2

$- 2$ .

\frac{- 2 s}{- 2} = \frac{6}{- 2}

$\frac{- 2 s}{- 2} = \frac{6}{- 2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 2 s}{- 2} = \frac{6}{- 2}$

Step 4.3.2.1.2

Divide

$s$ by

$1$ .

$s = \frac{6}{- 2}$

$s = \frac{6}{- 2}$

$s = \frac{6}{- 2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide

$6$ by

$- 2$ .

$s = - 3$

$s = - 3$

$s = - 3$

$s = - 3$

Step 5

Solve

$s - 1 = - (3 s + 5)$ for

$s$ .

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Step 5.1

Simplify

$- (3 s + 5)$ .

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Step 5.1.1

Rewrite.

$s - 1 = 0 + 0 - (3 s + 5)$

Step 5.1.2

Simplify by adding zeros.

$s - 1 = - (3 s + 5)$

Step 5.1.3

Apply the distributive property.

$s - 1 = - (3 s) - 1 \cdot 5$

Step 5.1.4

Multiply.

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Step 5.1.4.1

Multiply

$3$ by

$- 1$ .

$s - 1 = - 3 s - 1 \cdot 5$

Step 5.1.4.2

Multiply

$- 1$ by

$5$ .

$s - 1 = - 3 s - 5$

$s - 1 = - 3 s - 5$

$s - 1 = - 3 s - 5$

Step 5.2

Move all terms containing

$s$ to the left side of the equation.

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Step 5.2.1

Add

$3 s$ to both sides of the equation.

$s - 1 + 3 s = - 5$

Step 5.2.2

Add

$s$ and

$3 s$ .

$4 s - 1 = - 5$

$4 s - 1 = - 5$

Step 5.3

Move all terms not containing

$s$ to the right side of the equation.

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Step 5.3.1

Add

$1$ to both sides of the equation.

$4 s = - 5 + 1$

Step 5.3.2

Add

$- 5$ and

$1$ .

$4 s = - 4$

$4 s = - 4$

Step 5.4

Divide each term in

$4 s = - 4$ by

$4$ and simplify.

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Step 5.4.1

Divide each term in

$4 s = - 4$ by

$4$ .

$\frac{4 s}{4} = \frac{- 4}{4}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of

$4$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{4 s}{4} = \frac{- 4}{4}$

Step 5.4.2.1.2

Divide

$s$ by

$1$ .

$s = \frac{- 4}{4}$

$s = \frac{- 4}{4}$

$s = \frac{- 4}{4}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide

$- 4$ by

$4$ .

$s = - 1$

$s = - 1$

$s = - 1$

$s = - 1$

Step 6

List all of the solutions.

$s = - 3, - 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$