Question

PLEASE HELP!

Answer 1

Equations with absolute value:

$|f(x)| = k$

Where k is a positive number; if k is a negative number, the equation is impossible (absolute value is always positive).

How to solve:

$|f(x) | = k$
$- f(x) = k \: \: or \: \: f(x) = k$

Then:
1. |x+7|=12
x+7=12 V -x-7=12
x=5 V -x=19
x=5 V x=-19
{-19, 5}

2. |2x+4|=8
2x+4=8 V -2x-4=8
2x=4 V -2x=12
x=2 V x=-6

3. 3|3k|=27
3×3k=27 V 3×(-3k)=27
9k=27 V -9k=27
k=3 V k=-3
{-3, 3}

4. 5|b+8|=30
5×(b+8)=30 V 5×(-b-8)=30
5b+40=30 V -5b-40=30
5b=-10 V -5b=70
b=-2 V b=-14
{-14, -2}

5. |m+9|=5
m+9=5 V -m-9=5
m+9=5 V m+9=-5

Answer 2

Answer:

Equations with absolute value:

Where k is a positive number; if k is a negative number, the equation is impossible (absolute value is always positive).

How to solve:

Then:

1. |x+7|=12

x+7=12 V -x-7=12

x=5 V -x=19

x=5 V x=-19

{-19, 5}

2. |2x+4|=8

2x+4=8 V -2x-4=8

2x=4 V -2x=12

x=2 V x=-6

3. 3|3k|=27

3×3k=27 V 3×(-3k)=27

9k=27 V -9k=27

k=3 V k=-3

{-3, 3}

4. 5|b+8|=30

5×(b+8)=30 V 5×(-b-8)=30

5b+40=30 V -5b-40=30

5b=-10 V -5b=70

b=-2 V b=-14

{-14, -2}

5. |m+9|=5

m+9=5 V -m-9=5

m+9=5 V m+9=-5

Step-by-step explanation: