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How do you solve and graph #abs(10-3x)>=17#?

Answer 1

Kennedy Adams

The solution is #x in (-oo,-7/3]uu [9,+oo)#

This is an inequality with absolute values

#|10-3x|>=17#

Therefore,

#{(10-3x>=17),(-10+3x>=17):}#

#<=>#, #{(3x<=10-17),(3x>=17+10):}#

#<=>#, #{(x<=-7/3),(x>=9):}#

The solution is

#x in (-oo,-7/3]uu [9,+oo)#

The graph is

graph{|10-3x|-17 [-25.5, 25.83, -17.22, 8.43]}

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Answer 2

Julia Adams

To solve and graph the inequality |10 - 3x| ≥ 17:

Split the inequality into two separate cases: 10 - 3x ≥ 17 and 10 - 3x ≤ -17.
Solve each inequality separately for x.
Plot the solutions on a number line.
Shade the regions where the inequality holds true.
The resulting graph will depict the solution set for the absolute value inequality.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and graph #abs(10-3x)&gt;=17#?

How do you solve and graph #abs(10-3x)>=17#?