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How do you graph and solve #2 abs(3x-8)>10#?

Answer 1

# 5/3 > x > 13/3#

If #abs(3x-8) > 5# then

#{: (color(black)("if " 3x-8 >= 0),color(white)("XXXXXXX"),color(black)("if " 3x-8 <0)), (bar(color(white)("XXXXXXXXXX")),,bar(color(white)("XXXXXXXXX"))), (3x-8 > 5,,8-3x > 5), (3x > 13,,5 > 3x), (x > 13/3,,x < 5/3) :}#

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Answer 2

Kennedy Adams

To graph and solve the inequality 2|3x - 8| > 10, first, isolate the absolute value expression by dividing both sides by 2. This yields |3x - 8| > 5. Next, split the inequality into two cases: 3x - 8 > 5 and 3x - 8 < -5. Solve each case separately to find the solution set for x. For the first case, solve 3x - 8 > 5 to get x > 13/3. For the second case, solve 3x - 8 < -5 to get x < 1. Therefore, the solution to the inequality is x < 1 or x > 13/3. To graph this solution on a number line, mark the points x = 1 and x = 13/3 and shade the regions to the left of 1 and to the right of 13/3.

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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 graph and solve #2 abs(3x-8)&gt;10#?

How do you graph and solve #2 abs(3x-8)>10#?