Algebra Examples

$| 3 k - 2 | = 2 | k + 2 |$

Step 1

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

$2 | k + 2 | = | 3 k - 2 |$

Step 2

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

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Step 2.1

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

$\frac{2 | k + 2 |}{2} = \frac{| 3 k - 2 |}{2}$

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.

$\frac{2 | k + 2 |}{2} = \frac{| 3 k - 2 |}{2}$

Step 2.2.1.2

Divide $| k + 2 |$ by $1$ .

$| k + 2 | = \frac{| 3 k - 2 |}{2}$

Step 3

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

$k + 2 = \frac{3 k - 2}{2}$

$k + 2 = - \frac{3 k - 2}{2}$

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

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

Step 4

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

$k + 2 = \frac{3 k - 2}{2}$

$k + 2 = - \frac{3 k - 2}{2}$

Step 5

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

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Step 5.1

Multiply both sides by $2$ .

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

Step 5.2

Simplify.

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Step 5.2.1

Simplify the left side.

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Step 5.2.1.1

Simplify $(k + 2) \cdot 2$ .

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Step 5.2.1.1.1

Apply the distributive property.

$k \cdot 2 + 2 \cdot 2 = \frac{3 k - 2}{2} \cdot 2$

Step 5.2.1.1.2

Simplify the expression.

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Step 5.2.1.1.2.1

Move $2$ to the left of $k$ .

$2 \cdot k + 2 \cdot 2 = \frac{3 k - 2}{2} \cdot 2$

Step 5.2.1.1.2.2

Multiply $2$ by $2$ .

$2 k + 4 = \frac{3 k - 2}{2} \cdot 2$

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Cancel the common factor of $2$ .

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Step 5.2.2.1.1

Cancel the common factor.

$2 k + 4 = \frac{3 k - 2}{2} \cdot 2$

Step 5.2.2.1.2

Rewrite the expression.

$2 k + 4 = 3 k - 2$

Step 5.3

Solve for $k$ .

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Step 5.3.1

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

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Step 5.3.1.1

Subtract $3 k$ from both sides of the equation.

$2 k + 4 - 3 k = - 2$

Step 5.3.1.2

Subtract $3 k$ from $2 k$ .

$- k + 4 = - 2$

Step 5.3.2

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

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Step 5.3.2.1

Subtract $4$ from both sides of the equation.

$- k = - 2 - 4$

Step 5.3.2.2

Subtract $4$ from $- 2$ .

$- k = - 6$

Step 5.3.3

Divide each term in $- k = - 6$ by $- 1$ and simplify.

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Step 5.3.3.1

Divide each term in $- k = - 6$ by $- 1$ .

$\frac{- k}{- 1} = \frac{- 6}{- 1}$

Step 5.3.3.2

Simplify the left side.

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Step 5.3.3.2.1

Dividing two negative values results in a positive value.

$\frac{k}{1} = \frac{- 6}{- 1}$

Step 5.3.3.2.2

Divide $k$ by $1$ .

$k = \frac{- 6}{- 1}$

Step 5.3.3.3

Simplify the right side.

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Step 5.3.3.3.1

Divide $- 6$ by $- 1$ .

$k = 6$

Step 6

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

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Step 6.1

Multiply both sides by $2$ .

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

Step 6.2

Simplify.

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Step 6.2.1

Simplify the left side.

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Step 6.2.1.1

Simplify $(k + 2) \cdot 2$ .

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Step 6.2.1.1.1

Apply the distributive property.

$k \cdot 2 + 2 \cdot 2 = - \frac{3 k - 2}{2} \cdot 2$

Step 6.2.1.1.2

Simplify the expression.

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Step 6.2.1.1.2.1

Move $2$ to the left of $k$ .

$2 \cdot k + 2 \cdot 2 = - \frac{3 k - 2}{2} \cdot 2$

Step 6.2.1.1.2.2

Multiply $2$ by $2$ .

$2 k + 4 = - \frac{3 k - 2}{2} \cdot 2$

Step 6.2.2

Simplify the right side.

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Step 6.2.2.1

Simplify $- \frac{3 k - 2}{2} \cdot 2$ .

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Step 6.2.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.2.1.1.1

Move the leading negative in $- \frac{3 k - 2}{2}$ into the numerator.

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

Step 6.2.2.1.1.2

Cancel the common factor.

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

Step 6.2.2.1.1.3

Rewrite the expression.

$2 k + 4 = - (3 k - 2)$

Step 6.2.2.1.2

Apply the distributive property.

$2 k + 4 = - (3 k) - - 2$

Step 6.2.2.1.3

Multiply.

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Step 6.2.2.1.3.1

Multiply $3$ by $- 1$ .

$2 k + 4 = - 3 k - - 2$

Step 6.2.2.1.3.2

Multiply $- 1$ by $- 2$ .

$2 k + 4 = - 3 k + 2$

Step 6.3

Solve for $k$ .

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Step 6.3.1

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

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Step 6.3.1.1

Add $3 k$ to both sides of the equation.

$2 k + 4 + 3 k = 2$

Step 6.3.1.2

Add $2 k$ and $3 k$ .

$5 k + 4 = 2$

Step 6.3.2

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

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Step 6.3.2.1

Subtract $4$ from both sides of the equation.

$5 k = 2 - 4$

Step 6.3.2.2

Subtract $4$ from $2$ .

$5 k = - 2$

Step 6.3.3

Divide each term in $5 k = - 2$ by $5$ and simplify.

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Step 6.3.3.1

Divide each term in $5 k = - 2$ by $5$ .

$\frac{5 k}{5} = \frac{- 2}{5}$

Step 6.3.3.2

Simplify the left side.

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Step 6.3.3.2.1

Cancel the common factor of $5$ .

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Step 6.3.3.2.1.1

Cancel the common factor.

$\frac{5 k}{5} = \frac{- 2}{5}$

Step 6.3.3.2.1.2

Divide $k$ by $1$ .

$k = \frac{- 2}{5}$

Step 6.3.3.3

Simplify the right side.

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Step 6.3.3.3.1

Move the negative in front of the fraction.

$k = - \frac{2}{5}$

Step 7

List all of the solutions.

$k = 6, - \frac{2}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$k = 6, - \frac{2}{5}$

Decimal Form:

$k = 6, - 0.4$