can anyone explain how to solve this? I have no teacher to help me

## |5t - 7| = 11

# 2 Answers

Let's start with definition of absolute value

1. **l** a
**l** = a , if a ≥ 0 (if "a" is positive or 0) , for example

**l** 5
**l** = 5

2. **l** a
**l** = -a , if a < 0 (if "a" is negative) , for example

**l** -5
**l** = - (-5) = 5
*So, absolute value is always positive or zero*.

So, we need to consider two cases, because expression contain variable and can be positive, or negative

1. Let's assume that (5t - 7) ≥ 0 , then 5t - 7 = 11 ---> 5t = 18 --->** t _{1} = 18/5**

2. If (5t - 7) < 0 , then we have to put the "–" before (5t - 7)

– (5t - 7) = 11 or we can write 5t - 7 = -11 ---> 5t = -4 --->

**t**

_{2}= - 4/5Now let's check our answer

**l**5 · (18/5) - 7

**l**= 11

11 = 11

**l**5 · (-4/5) - 7

**l**= 11

11 = 11

Since |+/-11| = 11, there are two solutions for 5t-7.

5t-7 = 11 => t = 18/5

or

5t-7 = -11 => t = -4/5

Answer: t = 18/5 or -4/5