Question

Could somebody please help me show my work?
I have the right answer the question, I just need to show how I got that answer..

1. Which values of a and b are a solution to the inequality I 5 - 2a I - B < = 4?

Answer: a = 3, b = -1

Answer 1

\(\large{|5-2a| - b \le 4}\)

Can you first tell me how you got the answer ?

Answer 2

@Mclovin21 are you there?

Answer 3

yes, the teacher give us the answers and we have to show the work

Answer 4

Ohh so did you try the question first ?

Answer 5

yes

Answer 6

Can you show me you work please ?

Answer 7

I 5 -2a I - b <= 4
5 - 2 x 3- -1 <= 4
5 - 6 - -1 <= 4
-1 - -1 <= 4
0 <= 4


I think it's correct ... but, i'm not sure

Answer 8

@Mclovin21 were there options given in this question ?

Answer 9

a. a = 6, b = -2
b. a = -4, b = 3
c. a = 3, b = -1
d. a = -3, b = 5

Answer 10

By the way you did one mistake in your solution.

\(\color{blue}{\text{Originally Posted by}}\) @Mclovin21
I 5 -2a I - b <= 4
\(\color{red}|5 - 2 * 3\color{red}|-\color{red}( -1\color{red}) \le 4\)
5 - 6 - -1 <= 4
-1 - -1 <= 4
0 <= 4


I think it's correct ... but, i'm not sure
\(\color{blue}{\text{End of Quote}}\)

Answer 11

so I was correct just a few sign errors

Answer 12

Okay see the symbols I have added in red colour are very important:

(1) You forgot to take the absolute value of (5-2a).

This made your solution wrong.

Answer 13

ohhh how do you find the absolute value of it?

Answer 14

The correct solution would have been this:

\(\color{blue}{\text{Originally Posted by}}\) @Mclovin21
\(|5 -2a| - b \le 4\)
\(\color{red}|5 - 2 * 3\color{red}|- \color{red}(-1\color{red}) \le 4\)
\(\color{red}|5 - 6\color{red}| - \color{red}(-1\color{red}) \le 4\)
\(\color{red}|-1\color{red}| -\color{red}(-1\color{red}) \le 4\)
\(\color{red}1 + 1 \le 4\)
\(\color{red}2 \le 4\)

I think it's correct ... but, i'm not sure
\(\color{blue}{\text{End of Quote}}\)

Answer 15

ohhhhh okay! I see it now thank you!

Answer 16

Absolute value is just like a machine in which you insert a number and it gives the positive value of the same number in the output.

For example,

\(|2| = 2\) (Since, 2 is already positive so it didn't affect it and showed the same number)

\(|-2| = 2\) (Since, -2 is negative it changed it to 2\)

Basically,

\(|x| = x, \text{If x is positive}\)
and
\(|x| = -x, \text{If x is negative}\)

So, in the question you had

\(|-1|\) , now, -1 is negative so, the second part of definition will follow, that is

\(|-1| = \color{red}-\color{blue}(\color{green}{-1}\color{blue}) = \color{pink}1\)

Answer 17

No problem @Mclovin21 .

Best of luck

Good day