Step-by-step answer:
All the problems use absolute value function |x|
|x| means the positive value of x. That means |x| = |-x|
For example, |23| = |-23| = 23 (positive value)
In solving linear equations with absolute value functions, we generally have two solutions, for example:
|x+1| =7 mean we solve for x in
(x+1) = 7 => x=6, (when x+1 >0)
or
-(x+1) = 7 => x=-8 (when x+1<0)
So the solution is x=6 or x=-9
Q20:
Given: a=-2, b=-3, c=2, x=2.1, y=3, z=-4.2
Evaluate -3|z| + 2 (a + y)
Solution:
Substitute values, namely
-3|z| + 2 (a + y)
= -3 |-4.2|
In solving linear equations with absolute value functions, we generally have two solutions, for example:
|x+1| =7 mean we solve for x in
(x+1) = 7 => x=6, (when x+1 >0)
or
-(x+1) = 7 => x=-8 (when x+1<0)
So the solution is x=6 or x=-9
Q23:
|f+10|=1
when f+10 > 0 : (f+10) = 1 => f+10 = 1 => f = 1 - 10 => f = -9
when f+10 < 0 : -(f+10) = 1 => -f -10 = 1 => -f = 1+10 => -f = 11 => f = -11
The solution is therefore f = { -9, -11 }
Q24:
| v-2 | = -5
when v-2 > 0 : (v-2) = -5 => v-2 = -5 => v=-5+2 => v = -3
when v-2 < 0 : -(v-2) = -5 => -v +2 = -5 => -v = -5-2 => v = 7
The solution is therefore v = {-3, 7}
Q25:
| 4t-8 | = 20
when 4t-8 > 0 : (4t-8) = 20 => 4t = 20+8 => 4t=28 => t=7
when 4t-8 < 0 : -(4t-8) = 20 => -4t +8 = 20 => -4t = 20-8 => -4t = 12 => t = -3
The solution is therefore t = { 7, -3 }
