Algebra Examples

$| 4 h - 2 | = 2 | h + 3 |$

Step 1

Rewrite the equation as $2 | h + 3 | = | 4 h - 2 |$ .

$2 | h + 3 | = | 4 h - 2 |$

Step 2

Divide each term in $2 | h + 3 | = | 4 h - 2 |$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 | h + 3 | = | 4 h - 2 |$ by $2$ .

$\frac{2 | h + 3 |}{2} = \frac{| 4 h - 2 |}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 | h + 3 |}{2} = \frac{| 4 h - 2 |}{2}$

Step 2.2.1.2

Divide $| h + 3 |$ by $1$ .

$| h + 3 | = \frac{| 4 h - 2 |}{2}$

Step 3

Rewrite the absolute value equation as four equations without absolute value bars.

$h + 3 = \frac{4 h - 2}{2}$

$h + 3 = - \frac{4 h - 2}{2}$

$- (h + 3) = \frac{4 h - 2}{2}$

$- (h + 3) = - \frac{4 h - 2}{2}$

Step 4

After simplifying, there are only two unique equations to be solved.

$h + 3 = \frac{4 h - 2}{2}$

$h + 3 = - \frac{4 h - 2}{2}$

Step 5

Solve $h + 3 = \frac{4 h - 2}{2}$ for $h$ .

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Step 5.1

Cancel the common factor of $4 h - 2$ and $2$ .

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Step 5.1.1

Factor $2$ out of $4 h$ .

$h + 3 = \frac{2 (2 h) - 2}{2}$

Step 5.1.2

Factor $2$ out of $- 2$ .

$h + 3 = \frac{2 (2 h) + 2 \cdot - 1}{2}$

Step 5.1.3

Factor $2$ out of $2 (2 h) + 2 (- 1)$ .

$h + 3 = \frac{2 (2 h - 1)}{2}$

Step 5.1.4

Cancel the common factors.

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Step 5.1.4.1

Factor $2$ out of $2$ .

$h + 3 = \frac{2 (2 h - 1)}{2 (1)}$

Step 5.1.4.2

Cancel the common factor.

$h + 3 = \frac{2 (2 h - 1)}{2 \cdot 1}$

Step 5.1.4.3

Rewrite the expression.

$h + 3 = \frac{2 h - 1}{1}$

Step 5.1.4.4

Divide $2 h - 1$ by $1$ .

$h + 3 = 2 h - 1$

Step 5.2

Solve for $h$ .

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Step 5.2.1

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

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Step 5.2.1.1

Subtract $2 h$ from both sides of the equation.

$h + 3 - 2 h = - 1$

Step 5.2.1.2

Subtract $2 h$ from $h$ .

$- h + 3 = - 1$

Step 5.2.2

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

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Step 5.2.2.1

Subtract $3$ from both sides of the equation.

$- h = - 1 - 3$

Step 5.2.2.2

Subtract $3$ from $- 1$ .

$- h = - 4$

Step 5.2.3

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

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Step 5.2.3.1

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

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

Step 5.2.3.2

Simplify the left side.

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Step 5.2.3.2.1

Dividing two negative values results in a positive value.

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

Step 5.2.3.2.2

Divide $h$ by $1$ .

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

Step 5.2.3.3

Simplify the right side.

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Step 5.2.3.3.1

Divide $- 4$ by $- 1$ .

$h = 4$

Step 6

Solve $h + 3 = - \frac{4 h - 2}{2}$ for $h$ .

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Step 6.1

Cancel the common factor of $4 h - 2$ and $2$ .

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Step 6.1.1

Factor $2$ out of $4 h$ .

$h + 3 = - \frac{2 (2 h) - 2}{2}$

Step 6.1.2

Factor $2$ out of $- 2$ .

$h + 3 = - \frac{2 (2 h) + 2 \cdot - 1}{2}$

Step 6.1.3

Factor $2$ out of $2 (2 h) + 2 (- 1)$ .

$h + 3 = - \frac{2 (2 h - 1)}{2}$

Step 6.1.4

Cancel the common factors.

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Step 6.1.4.1

Factor $2$ out of $2$ .

$h + 3 = - \frac{2 (2 h - 1)}{2 (1)}$

Step 6.1.4.2

Cancel the common factor.

$h + 3 = - \frac{2 (2 h - 1)}{2 \cdot 1}$

Step 6.1.4.3

Rewrite the expression.

$h + 3 = - \frac{2 h - 1}{1}$

Step 6.1.4.4

Divide $2 h - 1$ by $1$ .

$h + 3 = - (2 h - 1)$

Step 6.2

Solve for $h$ .

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Step 6.2.1

Simplify $- (2 h - 1)$ .

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Step 6.2.1.1

Rewrite.

$h + 3 = 0 + 0 - (2 h - 1)$

Step 6.2.1.2

Simplify by adding zeros.

$h + 3 = - (2 h - 1)$

Step 6.2.1.3

Apply the distributive property.

$h + 3 = - (2 h) - - 1$

Step 6.2.1.4

Multiply.

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Step 6.2.1.4.1

Multiply $2$ by $- 1$ .

$h + 3 = - 2 h - - 1$

Step 6.2.1.4.2

Multiply $- 1$ by $- 1$ .

$h + 3 = - 2 h + 1$

Step 6.2.2

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

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Step 6.2.2.1

Add $2 h$ to both sides of the equation.

$h + 3 + 2 h = 1$

Step 6.2.2.2

Add $h$ and $2 h$ .

$3 h + 3 = 1$

Step 6.2.3

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

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Step 6.2.3.1

Subtract $3$ from both sides of the equation.

$3 h = 1 - 3$

Step 6.2.3.2

Subtract $3$ from $1$ .

$3 h = - 2$

Step 6.2.4

Divide each term in $3 h = - 2$ by $3$ and simplify.

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Step 6.2.4.1

Divide each term in $3 h = - 2$ by $3$ .

$\frac{3 h}{3} = \frac{- 2}{3}$

Step 6.2.4.2

Simplify the left side.

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Step 6.2.4.2.1

Cancel the common factor of $3$ .

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Step 6.2.4.2.1.1

Cancel the common factor.

$\frac{3 h}{3} = \frac{- 2}{3}$

Step 6.2.4.2.1.2

Divide $h$ by $1$ .

$h = \frac{- 2}{3}$

Step 6.2.4.3

Simplify the right side.

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Step 6.2.4.3.1

Move the negative in front of the fraction.

$h = - \frac{2}{3}$

Step 7

List all of the solutions.

$h = 4, - \frac{2}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$h = 4, - \frac{2}{3}$

Decimal Form:

$h = 4, - 0.\overline{6}$