Question

Solve.

2 |2x-7| + 11 <- 25

Answer 1

\[2 |2x-7| + 11 \le 25\]

Answer 2

when dealing with absolute values, you end up with two solutions
when x is less than zero
when x is greater than zero
so if for example you have
|x-3|
it would then be
x-3 **** this is greater than zero
-(x-3) = -x + 3 **** this is less than zero

Answer 3

the rest would be similar to solving any equality or inequality.

Answer 4

let me know if you need further clarification

Answer 5

i dont get it. :O

Answer 6

so i must multiply the |2x-7| with positive and negative?

Answer 7

with positive 1 for one solution and with negative 1 with the other solution

Answer 8

i see.. let me try to solve it..

Answer 9

okay put it here so I can see it

Answer 10

okay..
here..

\[2 |2x-7| + 11 \le 25\]
\[2 +1(2x-7) + 11 \]
\[2+2x-7+11 \le 25\]
\[2x+6 \le 25\]
is this right?

Answer 11

that's for +1

Answer 12

you should avoid using the plus and minus sign, because they can be mistaken for addition and subtraction, which is not the case
the 2 outside the | | means to multiply

2 |2x-7| +11 <=25
becomes
when x is greater than zero
2 (2x -7) + 11 <=25

when x is less than zero
2 [-1(2x-7)]+11<=25

Answer 13

ahh.. i see. .okey
:D

Answer 14

when x is greater than zero, nothing changes, you just copy whatever is inside the absolute bars and proceed with the operation.

Answer 15

my answer with postive is 4x <_ 27

Answer 16

and with negative is x <_ 0

Answer 17

double check

Answer 18

okie..

Answer 19

is it already correct?

Answer 20

when x is greater than 0
4x-14+11 <= 25
4x -3 <= 25
4x <= 28

Answer 21

-14+11= 2

Answer 22

oopsppss im wrong sorry.

Answer 23

4x ≤ 28 will i divide both sides by 4?

Answer 24

when x is less than zero
2 [-1(2x-7)]+11<=25
2(-2x+7)+11<=25
-4x+14+11<=25
-4x+25<=25
-4x<=0

Answer 25

can X be a -x?

Answer 26

it cannot
you are solving for x not -x
so when it is -x you multiply it by -1 to undo the negative
when it is -4, you divide it by -4
but when dividing an inequality by a negative you will need to flip the inequality from greater than to less than, from less than to greater than, from greater than or equal to to less than or equal to, from less than or equal to to greater than or equal to

Answer 27

do you have any lecture notes?
these are fundamental that you should have learned a while ago

Answer 28

ooh.. i see.. then 4x ≤ 28 i should divide both sides by 4?

Answer 29

yes

Answer 30

thx,