Question

The table below shows two equations:

Equation 1 |3x – 1| + 7 = 2
Equation 2 |2x + 1| + 4 = 3


Which statement is true about the solution to the two equations

Answer 1

Equation 1 and equation 2 have no solutions.

Equation 1 has no solution and equation 2 has solutions x = 0, 1.

The solutions to equation 1 are x = -1.3, 2 and equation 2 has no solution.

The solutions to equation 1 are x = -1.3, 2 and equation 2 has solutions x = 0, 1.

Answer 2

what do you know about absolute values?

Answer 3

its a numbers distance from 0

Answer 4

what is the smallest value |3x+1| and |2x+1| can be?

Answer 5

i dont understand the whole absolute value thing they tried to teach me it when i went to the high school and i didnt understand it

Answer 6

distance is a good analogy... is distance ever negative?

Answer 7

you there?

Answer 8

@pgpilot326 sorry got caught up doing something no distance is not negative

Answer 9

so the smallest they can be is 0, right?

Answer 10

yes

Answer 11

so look at the first equation.

is there any way to get the left hand side to be equal to 2?

Answer 12

subtract the 1 by the 3?

Answer 13

remember, the smallest |3x-1| can be is 0.

0+7=7 is the smallest the left hand side can be no matter what x is.

another way to approach it is to first subtract 7 from both sides.

the we get |3x-1|=-5. again, remember that the smallest |3x-1| can be is 0, no matter what x is.
So is there any x that will make |3x-1|=-2?

Answer 14

no

Answer 15

excellent!

no follow the same logic/steps with the next equation. what do you find?

Answer 16

"now" not "no"

Answer 17

|2x+1|=-1

Answer 18

is there any x that will make that true?

Answer 19

no

Answer 20

excellent!

so if there aren't any values of x to satisfy an equation, we say that equation has no solution.

Answer 21

so 1 and 2 have no solution

Answer 22

marvelous!!!

Answer 23

thanks for the help!

Answer 24

you're welcome!