Solve absolute value inequality. |2-x/2|-1\le 1

chezmarylou1i

chezmarylou1i

Answered question

2021-12-06

Solve absolute value inequality.
|2x2|11

Answer & Explanation

Papilys3q

Papilys3q

Beginner2021-12-07Added 34 answers

Step 1
We have to solve the absolute value inequality:
|2x2|11
Adding 1 both sides,
|2x2|11
|2x2|1+11+1
|2x2|2
Step 2
We know that
if |x|a then axa
Therefore for |2x2|2,
22x22
Subtracting 2 each sides,
222x2222
4x20
We know that if we multiply by negative quantity then sign of inequality get changed.
Multiplying by −1,
4(1)x2(1)0(1)
4x20
0x24
Multiplying by 2,
2×0x2×24×2
0x8
Hence, solution of the inequality is x[0,8].

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