Algebra Examples

$| 2 x + 7 | - k \leq 5$

Step 1

Subtract $| 2 x + 7 |$ from both sides of the inequality.

$- k \leq 5 - | 2 x + 7 |$

Step 2

Divide each term in $- k \leq 5 - | 2 x + 7 |$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- k \leq 5 - | 2 x + 7 |$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- k}{- 1} \geq \frac{5}{- 1} + \frac{- | 2 x + 7 |}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{k}{1} \geq \frac{5}{- 1} + \frac{- | 2 x + 7 |}{- 1}$

Step 2.2.2

Divide $k$ by $1$ .

$k \geq \frac{5}{- 1} + \frac{- | 2 x + 7 |}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $5$ by $- 1$ .

$k \geq - 5 + \frac{- | 2 x + 7 |}{- 1}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$k \geq - 5 + \frac{| 2 x + 7 |}{1}$

Step 2.3.1.3

Divide $| 2 x + 7 |$ by $1$ .

$k \geq - 5 + | 2 x + 7 |$