How do you solve | 2x + 5 | < 13?

Question

Which of these could be correct?

a. -8 < x < 5

b. -5 < x < 8

c. 5 < x < 8

d. -8 < x < -5

or is it none of these ?

Answer 1

Note first that |2x = 5| = |2x - (-5)|.

Next, think of the absolute value of a difference as a distance and the problem as being equivalent to:

find the values of x where the distance from 2x to (-5) is less than 13.

--> then (-5) -13 < 2x < (-5) +13

or

-18 < 2x < 8

or

-9 < x < 4.

So, the answer is 'none of these'.

Answer 2

1st take every thing out of absolute value bars.
So it will be

2x+5<13

Subtract 5 from both sides

2x+5<13
-5 -5
2x+0<8

Divide 2 by both sides

2x/2<8/2
x=4
So to fix the answer you minus 5 which is -5 and we know x is 4 and -5 is<4 and when we had subtracted 5 from 13 we got 8 and 4 is <8.
It should look like this

-5<4<8

Answer 3

Hi,

| 2x + 5 | < 13

-13 < 2x + 5 < 13
- 18 < 2x < 8
-9 < x < 4

So none of the choices given in the problem are correct.

Good luck

Answer 4

Strictly speaking 2x + 5 < 13 => x < 4 besides the fact that it additionally has a cap at x > -9 => |2(-9) + 5| = 13 subsequently, -9 < x < 4 could desire to be your answer. via removing, a. via attempting 4, we get 13 < 13 which isn't genuine b. via attempting 7, we get 19 < 13, which isn't genuine c. comparable as b. d. it quite works yet no longer the full selection e. i could choose this. besides the fact that it relies upon if this could be a severe question or a trick question as d is likewise a available answer.

Answer 5

This inequality can be changed to
-13 < (2x+5) < 13

Now isolate x by subtracting 5 from all three places and dividing everything by 2

-18 < 2x < 8
-9 < x < 4

Answer 6

it is none of these the correct answer is -9 the above qwes. means that 2x+5 can be less than 13 or greater than -13 now solving the two you can get the answer

-13<(2x+5)<13
adding -5 to each side
-18<2x<8
dividing each side by 2
-9

Answer 7

| 2x + 5 | < 13

To solve this, note that an absolute inequality in the form
|z| < c (for positive constant c) equates to the following inequality:

-c < z < c

Same deal here.

|2x + 5| < 13
-13 < 2x + 5 < 13

Now, isolate x as per the usual methods. Subtract 5 to the inequality gives us

-18 < 2x < 8

Divide by 2,

-9 < x < 4

Answer 8

| 2x + 5 | < 13
solve positive
2x + 5 < 13
2x < 8
x < 4
and negative
2x + 5 > -13
2x > -18
x > -9
then put them together
-9 < x < 4

Answer 9

If 2x+5>0 so x> -5/2
2x+5>13 snd x >4
If 2x+5<=0 so x<=-5/2
-2x-5<13 so 2x >-18 and x>-9
The solution is
-94
By error I solved I2x+5I>13 but the proceedings are the same

Answer 10

With the "less than" sign, there is no definitive value for x.
The equation becomes 2x<8, then x<4; so x can be 1, 2 or 3.