Finite Math Examples

$3 | w + 1 | - 2 = 7$

Step 1

Move all terms not containing $| w + 1 |$ to the right side of the equation.

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Step 1.1

Add $2$ to both sides of the equation.

$3 | w + 1 | = 7 + 2$

Step 1.2

Add $7$ and $2$ .

$3 | w + 1 | = 9$

Step 2

Divide each term in $3 | w + 1 | = 9$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 | w + 1 | = 9$ by $3$ .

$\frac{3 | w + 1 |}{3} = \frac{9}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 | w + 1 |}{3} = \frac{9}{3}$

Step 2.2.1.2

Divide $| w + 1 |$ by $1$ .

$| w + 1 | = \frac{9}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $9$ by $3$ .

$| w + 1 | = 3$

Step 3

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

$w + 1 = \pm 3$

Step 4

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

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Step 4.1

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

$w + 1 = 3$

Step 4.2

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

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Step 4.2.1

Subtract $1$ from both sides of the equation.

$w = 3 - 1$

Step 4.2.2

Subtract $1$ from $3$ .

$w = 2$

Step 4.3

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

$w + 1 = - 3$

Step 4.4

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

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Step 4.4.1

Subtract $1$ from both sides of the equation.

$w = - 3 - 1$

Step 4.4.2

Subtract $1$ from $- 3$ .

$w = - 4$

Step 4.5

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

$w = 2, - 4$