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Help me please i keep getting stuck on this question

Help me please i keep getting stuck on this question-example-1

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4 votes

Answer:

-3 <= x <=8

Explanation:

-16 -3|2x-5| >= -49

The first step is to get the absolute value alone. We need to add 16 to each side.

-16+16 -3|2x-5| >= -49+16

-3|2x-5| >= -33

Now divide each side by -3. This will flip the inequality.

(-3/-3)|2x-5| =< -33/-3

|2x-5| =< 11

This is where we can separate the absolute value inequality into 2 pieces, one positive and one negative. Remember to flip the inequality symbol when we take the negative inequality.

2x-5 <=11 and 2x-5>=-11

Add 5 to each side.

2x-5+5 <=11+5 and 2x-5+5>=-11+5

2x<=16 and 2x>=-6

Divide by 2 on each side.

2x/2<=16/2 and 2x/2>=-6/2

x <=8 and x >=-3

Rewrite as a compound inequality

-3 <= x <=8

User JohanSJA
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