How do you solve |x+1|+1≥8?

2 Answers
smendyka
Mar 18, 2018

See a solution process below:

Explanation:

First, subtract 1 from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

|x+1|+1−1≥8−1

|x+1|≥7

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

−7≥x+1≥7

Now, subtract 1 from each segment of the system of inequalities to solve for x while keeping the system balanced:

−7−1≥x+1−1≥7−1

−8≥x+0≥6

−8≥x≥6

Or

x≤−8; x≥6

Or, in interval notation:

(−∞,−8]; [6,+∞)

Gazza
Mar 18, 2018

x≥6orx≤−8

Explanation:

|x+1|+1≥8

Let start by adding −1to both sides

|x+1|+1−1≥8−1

|x+1|≥7

We know either: x+1≥7orx+1≤−7

Let start with the first possibility which is:

x+1≥7

Add −1 on both sides

x+1−1≥7−1

x≥6

Now the second possibility

x+1≤−7

Add −1 on both sides

x+1−1≤−7−1

x≤−8

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