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How do you solve and graph #abs(2g-5)>=9#?

Answer 1

Avery Alexander

#x in (- infty, -2] cup [7, infty)#

#2g - 5 >= 9 or 2g - 5 <= -9#

#2g >= 14 or 2g <= -4#

#g >= 7 or g <= -2#

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Answer 2

Savannah Anderson

To solve and graph the inequality |2g - 5| ≥ 9:

Step 1: Break the inequality into two cases: Case 1: 2g - 5 ≥ 9 Case 2: -(2g - 5) ≥ 9

Step 2: Solve each case separately: Case 1: 2g - 5 ≥ 9 2g ≥ 9 + 5 2g ≥ 14 g ≥ 7

Case 2: -(2g - 5) ≥ 9 -2g + 5 ≥ 9 -2g ≥ 9 - 5 -2g ≥ 4 g ≤ -2

Step 3: Combine the solutions: g ≥ 7 or g ≤ -2

Step 4: Graph the solutions on a number line: ----------------|-----------|----------------- -∞ -2 7 +∞

Step 5: Since the inequality is greater than or equal to, we include solid dots at -2 and 7 to indicate that these values are included in the solution set. Then shade the regions to the right of 7 and to the left of -2.

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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(2g-5)&gt;=9#?

How do you solve and graph #abs(2g-5)>=9#?