Solve absolute value inequality. |2(x-1)+4|\leq8

sodni3

sodni3

Answered question

2021-02-25

Solve absolute value inequality.
|2(x1)+4|8

Answer & Explanation

Leonard Stokes

Leonard Stokes

Skilled2021-02-26Added 98 answers

Step 1
We have to solve the absolute value inequality:
|2(x1)+4|8
We know for any modulus function,
|f(x)|={f(x)if f(x)0f(x)if f(x)<0
We also know that if |f(x)| a then it must satisfy that
af(x)a
Applying above condition for given inequality,
af(x)a
82(x1)+48
Step 2
Simplifying further,
842(x1)+4484 (substracted 4)
122(x1)4
1222(x1)242 (divided all sides by 2)
6(x1)2
6+1x1+12+1
5x3
In interval notation we can write it as x[5,3].
Hence, solution of the absolute value inequality is x[5,3].

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