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  1. |x|+5=18 (1 point)

A: 5 or -5

B: 13 or -13 (I think it's this one)

C: 18 or -18

D: 23 or -23

  1. |y+4|< 1 (1 point)

A: -5<y< -3 (i think its this one)
B: -3<y<5
C: -4<y<1
D: 1<y<4 

3. |2t|- 5=7

A: t=1 or -1

B: t=6 or -6 (i think it's this one)

C: t=10 or -10

D: t=12 or -12


           3     5

  1. |a| - - = - - (1 point)

4      8

1        1

A: -- or - -- (i think it's this one)

8       8


7        7

B: -- or - --

8         8


3         3

C: 1 -- or -1 --

8         8


D: No solution

Verified Answer :

samweli

the answer 1:B
2:A
3:B
4:A

The solutions to the given absolute value problems are;

1) Option B

2) Option A

3) Option B

4) Option A

  • This is an absolute value problem.

Absolute value is simply the distance on the number line from the origin regardless of whether it is positive or not.

  • 1) |x| + 5 = 18

Subtract 5 from both sides to get;

|x| = 13

Since it's absolute value, then it means that;

x = ± 13

Thus; x = 13 or -13

  • 2) |y + 4|< 1

Since it's absolute value, then it means that;

± (y + 4) < 1

Thus;

-y - 4 < 1 or y + 4 < 1

Simplifying gives;

-5 < y or y < -3

Thus combining both to get;

-5 < y < -3

  • 3) |2t| - 5 = 7

Add 5 to both sides to get;

|2t| = 12

Since absolute value, it means;

±2t = 12

-2t = 12 or +2t = 12

Simplifying gives;

t = -6 or 6

  • 4) |a| - ³/₄ = -⁵/₈

Add ³/₄ to both sides to get;

|a| = ¹/₈

Since absolute value, it means;

a = ¹/₈ or -¹/₈

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