Solve for h |3h+1|=7h

$| 3 h + 1 | = 7 h$

Step 1

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

$3 h + 1 = \pm 7 h$

Step 2

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.

$3 h + 1 = 7 h$

Move all terms containing $h$ to the left side of the equation.

Subtract $7 h$ from both sides of the equation.

$3 h + 1 - 7 h = 0$

Subtract $7 h$ from $3 h$ .

$- 4 h + 1 = 0$

Subtract $1$ from both sides of the equation.

$- 4 h = - 1$

Divide each term in $- 4 h = - 1$ by $- 4$ and simplify.

Divide each term in $- 4 h = - 1$ by $- 4$ .

$\frac{- 4 h}{- 4} = \frac{- 1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 h}{- 4} = \frac{- 1}{- 4}$

Divide $h$ by $1$ .

$h = \frac{- 1}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$h = \frac{1}{4}$

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

$3 h + 1 = - 7 h$

Move all terms containing $h$ to the left side of the equation.

Add $7 h$ to both sides of the equation.

$3 h + 1 + 7 h = 0$

Add $3 h$ and $7 h$ .

$10 h + 1 = 0$

Subtract $1$ from both sides of the equation.

$10 h = - 1$

Divide each term in $10 h = - 1$ by $10$ and simplify.

Divide each term in $10 h = - 1$ by $10$ .

$\frac{10 h}{10} = \frac{- 1}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 h}{10} = \frac{- 1}{10}$

Divide $h$ by $1$ .

$h = \frac{- 1}{10}$

Simplify the right side.

Move the negative in front of the fraction.

$h = - \frac{1}{10}$

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

$h = \frac{1}{4}, - \frac{1}{10}$

Step 3

Exclude the solutions that do not make $| 3 h + 1 | = 7 h$ true.

$h = \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$h = \frac{1}{4}$

Decimal Form:

$h = 0.25$

Solve for h |3h+1|=7h

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