Question

Solve the following inequality algebraically. |x - 7|>4

Answer 1

Given:

|x - 7| > 4

Let's solve the inequality for x using the following steps.

Step 1:

Find the inside of the absolute value when it is non-negative

x - 7 ≥ 0

Add 7 to both sides:

x - 7 + 7 ≥ 0 + 7

x ≥ 7

Find the inside of the absolute value when it is negative by multiplyin by -1:

-(x - 7) > 4

Step 2:

We have two conditions

x - 7 > 4

-(x - 7) > 4

Let's solve for x in both conditions.

We have:

`\begin{gathered} \begin{cases}x-7>4 \\ -(x-7)>4\end{cases} \\ \\ \end{gathered}`

Condition 1:

x - 7 > 4

Add 7 to both sides:

x - 7 + 7 > 4 + 7

x > 11

Condition 2:

-(x - 7) > 4

Apply distributive property:

-x - - 7 > 4

-x + 7 > 4

Subtract 7 from both sides:

-x + 7 - 7 > 4 - 7

-x > -3

Divide both sides by -1:

`\begin{gathered} (-x)/(-1)>(-3)/(-1) \\ \\ x<3 \end{gathered}`

ANSWER:

x < 3 or x > 11