Question

Which of the following is a solution for the absolute value inequality |2x-3|>6?

Answer 1

when you have => |2x-3|>6
what's really meant is
+1(2x-3)>6
AND
-1(2x-3)>6

so solve those 2 and get the values for "x" :)

Answer 2

i dont really know how to solve this. :/ can you help please?

Answer 3

well, let's try the 1st one
how would you solve
+1(2x-3) = 6

Answer 4

what would "x" give you?

Answer 5

Um, do you distribute the 1? Or minus the one on both sides?

Answer 6

well, in the 1st case, we have a +1, and you distribute inside the parentheses, yes

Answer 7

so it'd be 2x - 3 > 6?

Answer 8

yes, but solving for "x", "x" would be?

Answer 9

4.5 and -4.5 ?

Answer 10

well, the 1st case will give you ONLY 9/2 or 4.5
for the second case, you may try to solve for "x" at
-1(2x-3) = 6

Answer 11

what would that give you?

Answer 12

I really dont know..

Answer 13

-1(2x-3) = 6
-2x +3 = 6

Answer 14

-1.5

Answer 15

A. x=-1.46
B. x= 6.83
C. x=2 4/7
D. x= -1 3/8
are the ones to choose from

Answer 16

do u know it?

Answer 17

yes, -3/2
so in the 1st case what happened was
$$
|2x-3|>6\\
+1(2x-3)>6\\
2x-3 > 6 \implies 2x > 9 \implies x > \frac{9}{2}\\
-1(2x-3)>6\\
-2x+3 > 6 \implies -2x > 3\\
\text{the one thing you'd need to keep in mind}\\
\text{for inequalities, is that whenever you}\\
\text{divide or multiply or exponentialize by}\\
\text{a negative value, you have to}\text{ flip } \text{the sign, thus}\\
-2x > 3 \implies x \color{red}{<} -\frac{3}{2}
$$