Algebra Examples

| 3 x - 2 | = 5

$| 3 x - 2 | = 5$

Step 1

Remove the absolute value term. This creates a

\pm

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

| x | = \pm x

$| x | = \pm x$ .

3 x - 2 = \pm 5

$3 x - 2 = \pm 5$

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.

3 x - 2 = 5

$3 x - 2 = 5$

Step 2.2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.2.1

Add

2

$2$ to both sides of the equation.

3 x = 5 + 2

$3 x = 5 + 2$

Step 2.2.2

Add

5

$5$ and

2

$2$ .

3 x = 7

$3 x = 7$

3 x = 7

$3 x = 7$

Step 2.3

Divide each term in

3 x = 7

$3 x = 7$ by

3

$3$ and simplify.

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Step 2.3.1

Divide each term in

3 x = 7

$3 x = 7$ by

3

$3$ .

\frac{3 x}{3} = \frac{7}{3}

$\frac{3 x}{3} = \frac{7}{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of

3

$3$ .

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Step 2.3.2.1.1

Cancel the common factor.

\frac{3 x}{3} = \frac{7}{3}

$\frac{3 x}{3} = \frac{7}{3}$

Step 2.3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{7}{3}

$x = \frac{7}{3}$

x = \frac{7}{3}

$x = \frac{7}{3}$

x = \frac{7}{3}

$x = \frac{7}{3}$

x = \frac{7}{3}

$x = \frac{7}{3}$

Step 2.4

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

3 x - 2 = - 5

$3 x - 2 = - 5$

Step 2.5

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.5.1

Add

2

$2$ to both sides of the equation.

3 x = - 5 + 2

$3 x = - 5 + 2$

Step 2.5.2

Add

- 5

$- 5$ and

2

$2$ .

3 x = - 3

$3 x = - 3$

3 x = - 3

$3 x = - 3$

Step 2.6

Divide each term in

3 x = - 3

$3 x = - 3$ by

3

$3$ and simplify.

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Step 2.6.1

Divide each term in

3 x = - 3

$3 x = - 3$ by

3

$3$ .

\frac{3 x}{3} = \frac{- 3}{3}

$\frac{3 x}{3} = \frac{- 3}{3}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of

3

$3$ .

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Step 2.6.2.1.1

Cancel the common factor.

\frac{3 x}{3} = \frac{- 3}{3}

$\frac{3 x}{3} = \frac{- 3}{3}$

Step 2.6.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 3}{3}

$x = \frac{- 3}{3}$

x = \frac{- 3}{3}

$x = \frac{- 3}{3}$

x = \frac{- 3}{3}

$x = \frac{- 3}{3}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide

- 3

$- 3$ by

3

$3$ .

x = - 1

$x = - 1$

x = - 1

$x = - 1$

x = - 1

$x = - 1$

Step 2.7

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

x = \frac{7}{3}, - 1

$x = \frac{7}{3}, - 1$

x = \frac{7}{3}, - 1

$x = \frac{7}{3}, - 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

x = \frac{7}{3}, - 1

$x = \frac{7}{3}, - 1$

Decimal Form:

x = 2.\overline{3}, - 1

$x = 2.\overline{3}, - 1$

Mixed Number Form:

x = 2 \frac{1}{3}, - 1

$x = 2 \frac{1}{3}, - 1$

| 3 x - 2 | = 5

$| 3 x - 2 | = 5$

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

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