Solve absolute value inequality : -2|x-4|\geq -4

yapafw

yapafw

Answered question

2021-12-05

Solve absolute value inequality :
2|x4|4

Answer & Explanation

Fachur

Fachur

Beginner2021-12-06Added 17 answers

Step 1
Consider the inequality 2|x4|4
Multiply both the sides by the -1 then sign will be change,
(2|x4|)(1)4(1)
2|x4|4
Divide both the sides by 2,
2|x4|242
Simplifying further,
|x4|2...(1)
Absolute value cases always contain two cases,
Step 2
So,
x42 and x42
Case (1) we solve,
x42
x2+4
x6
Case (2) we solve,
x42
x2+4
x2
Hence, the combine interval is 2x6.

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