Solve the Absolute Value Inequality for y -2|7-3y|-6=-14

$- 2 | 7 - 3 y | - 6 = - 14$

Move all terms not containing $| 7 - 3 y |$ to the right side of the equation.

Add $6$ to both sides of the equation.

$- 2 | 7 - 3 y | = - 14 + 6$

Add $- 14$ and $6$ .

$- 2 | 7 - 3 y | = - 8$

Divide each term in $- 2 | 7 - 3 y | = - 8$ by $- 2$ and simplify.

Divide each term in $- 2 | 7 - 3 y | = - 8$ by $- 2$ .

$\frac{- 2 | 7 - 3 y |}{- 2} = \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 | 7 - 3 y |}{- 2} = \frac{- 8}{- 2}$

Divide $| 7 - 3 y |$ by $1$ .

$| 7 - 3 y | = \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$| 7 - 3 y | = 4$

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

$7 - 3 y = \pm 4$

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.

$7 - 3 y = 4$

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

Subtract $7$ from both sides of the equation.

$- 3 y = 4 - 7$

Subtract $7$ from $4$ .

$- 3 y = - 3$

Divide each term in $- 3 y = - 3$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 3$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 3$ .

$y = 1$

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

$7 - 3 y = - 4$

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

Subtract $7$ from both sides of the equation.

$- 3 y = - 4 - 7$

Subtract $7$ from $- 4$ .

$- 3 y = - 11$

Divide each term in $- 3 y = - 11$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 11$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 11}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 11}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 11}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{11}{3}$

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

$y = 1, \frac{11}{3}$

The result can be shown in multiple forms.

Exact Form:

$y = 1, \frac{11}{3}$

Decimal Form:

$y = 1, 3.\overline{6}$

Mixed Number Form:

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

Solve the Absolute Value Inequality for y -2|7-3y|-6=-14

Related Questions

Support LCMGCF.com by disabling your adblocker.