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Solve. Graph the solution and write the solution in interval notation.

2+|x−4|>6

2 Answers

1 vote

Final answer:

The solution to the inequality 2+|x-4|>6 in interval notation is (−∞,0)∪(8,+∞)

To solve the inequality 2+∣x−4∣>6 and express the solution in interval notation, follow these steps:

Subtract 2 from both sides of the inequality:∣x−4∣>6−2

Simplify: ∣x−4∣>4

To solve the absolute value inequality

∣x−4∣>4, set up two separate inequalities:

a. x−4>4 (when x−4 is positive)

b. −(x−4)>4 (when x−4 is negative)

Solve each inequality separately:

a. x−4>4

Add 4 to both sides:x>8

b.−(x−4)>4

Distribute the negative sign:−x+4>4

Subtract 4 from both sides:−x>0

Multiply both sides by -1 (this reverses the inequality):x<0

Combine the solutions:

The solution for x is x<0 or x>8.

Express the solution in interval notation:(−∞,0)∪(8,+∞)

User Todd Davies
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7.1k points
1 vote

Answer:

i graphed it for you

Explanation:

Solve. Graph the solution and write the solution in interval notation. 2+|x−4|&gt-example-1
User Gmazzo
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7.4k points