Question

I need help with 20, 23-25 please​

Answer 1

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 }