Question

Solve: |4x + 2| < 8 help me please

Answer 1

`(3)/(2)` or
`1.5`

Explanation:

1. Simplify: |4x + 2| < 8 = 4x + 2 < 8
2. Re-write it: 4x + 2 < 8
3. Subtract 2 from each side, so it now looks like this: 4x < 6
4. Divide each side by 4, to cancel out the 4 next to x. It should now look like this: x < 1.5

To get the fraction answer:

1. Covert 1.5 into a mixed number:
   `1(5)/(10)`
2. Covert 1 5/10 into an improper fraction: 1 × 10 = 10, 10 + 5 = 15
3. Right the new fraction: 15/10
4. Simplify by dividing each side by 5. It should now look like this: 3/2

Answer 2

-5/2 < x < 3/2

In interval notation: (-5/2, 3/2)

Explanation:

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Rule

To solve an absolute value inequality of the form

|X| < k

where X is an expression in x and k is a non-negative number,

solve the following compound inequality

-k < X < k

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For this problem, X is 4x + 2, an expression in x. k is 8.

Follow the rule above, and change the absolute value inequality

|4x + 2| < 8 into

-8 < 4x + 2 < 8

Now we solve the compound inequality.

Subtract 2 from the three sides.

-10 < 4x < 6

Divide the three sides by 4.

-10/4 < x < 6/4

Reduce the fractions.

-5/2 < x < 3/2

Answer:

-5/2 < x < 3/2

In interval notation: (-5/2, 3/2)