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- anonymous

PLEASE HELP ONE QUESTION WILL MEDAL AND FAN!

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- anonymous

PLEASE HELP ONE QUESTION WILL MEDAL AND FAN!

- katieb

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- anonymous

Solve and graph the absolute value inequality: |2x + 1| ≤ 5.
number line with closed dots on negative 3 and 2 with shading going in the opposite directions.
number line with closed dots on negative 3 and 2 with shading in between.
number line with open dots on negative 3 and 2 with shading in between.
number line with closed dots on negative 2 and 2 with shading in between.

- Hero

Hint:
|ax + b| ≤ c is equivalent to -c ≤ ax + b ≤ c

- anonymous

What????? So confused. Could you explain better?

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- Hero

In order to properly graph the absolute value inequality, you must first solve for x. The hint I gave you shows a mathematical statement equivalent to the given statement that allows you to solve for x, which in turn, will enable you to properly graph the inequality.

- anonymous

ok, so |2x + 1| ≤ 5. First, would i subtract one from each side?

- pooja195

Set up two equations
We know 2x+1≤5 and 2x+1≥−5
Solve for each
\[\huge~2x+1≤5 \]
\[\huge~2x+1≥−5\]

- anonymous

OK

- anonymous

2x+1<5
-1 -1
2x <4
/2 /2
x<2? for the first one?

- anonymous

2x+1>5
-1 -1
2x > 4
/2 /2
x>2 for the second one as well?

- pooja195

No.

- Hero

It's much easier to solve it as just one compound inequality:
-5 ≤ 2x + 1 ≤ 5
Subtract one from each side, then divide each side by two.

- anonymous

-6<2x<4?

- anonymous

with the line underneath the signs

- Hero

-6 ≤ 2x ≤ 4
Then divide each side by 2.

- anonymous

-3

- anonymous

with lines underneath

- Hero

-3 ≤ x ≤ 2

- Hero

The inequality basically states that the solution, x, exists between -3 and 2 (inclusive)

- anonymous

so B?

- Hero

Correct.

- anonymous

thank you so much!

- Hero

You're welcome.

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