Solve for w 3|4w-1|-5=10

$3 | 4 w - 1 | - 5 = 10$

Step 1

Move all terms not containing $| 4 w - 1 |$ to the right side of the equation.

Add $5$ to both sides of the equation.

$3 | 4 w - 1 | = 10 + 5$

Add $10$ and $5$ .

$3 | 4 w - 1 | = 15$

Step 2

Divide each term in $3 | 4 w - 1 | = 15$ by $3$ and simplify.

Divide each term in $3 | 4 w - 1 | = 15$ by $3$ .

$\frac{3 | 4 w - 1 |}{3} = \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | 4 w - 1 |}{3} = \frac{15}{3}$

Divide $| 4 w - 1 |$ by $1$ .

$| 4 w - 1 | = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$| 4 w - 1 | = 5$

Step 3

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

$4 w - 1 = \pm 5$

Step 4

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

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

$4 w - 1 = 5$

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

Add $1$ to both sides of the equation.

$4 w = 5 + 1$

Add $5$ and $1$ .

$4 w = 6$

Divide each term in $4 w = 6$ by $4$ and simplify.

Divide each term in $4 w = 6$ by $4$ .

$\frac{4 w}{4} = \frac{6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 w}{4} = \frac{6}{4}$

Divide $w$ by $1$ .

$w = \frac{6}{4}$

Simplify the right side.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$w = \frac{2 (3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$w = \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$w = \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$w = \frac{3}{2}$

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

$4 w - 1 = - 5$

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

Add $1$ to both sides of the equation.

$4 w = - 5 + 1$

Add $- 5$ and $1$ .

$4 w = - 4$

Divide each term in $4 w = - 4$ by $4$ and simplify.

Divide each term in $4 w = - 4$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $w$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $4$ .

$w = - 1$

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$w = 1.5, - 1$

Mixed Number Form:

$w = 1 \frac{1}{2}, - 1$

Solve for w 3|4w-1|-5=10

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