Question

PLEASE HELP!

Question 1
Solve the equation.
|x + 7| = 12
A. {-19, -5}
B. {-19, 5}
C. {-5, 19}
D. {5, 19}

Question 2
|2 x + 4| = 8
A. x = -12 or x = 4
B. x = -6 or x = 2
C. x = 2 only
D. x = 6 only

Question 3
3|3k| = 27
A. {-9, 9}
B. {-3, 3}
C. {-3, 9}
D. -3 < k < 3

Question 4
5|b + 8| = 30
A. {-2, 2}
B. {-14, 14}
C. {-14, -2}
D. {-10, 2}


Question 5
Which equations are equivalent to the open sentence |m + 9| = 5?
A. m + 9 = 5 and m + 9 = -5
B. m - 9 = 5 or m - 9 = -5
C. m + 9 = 5 and m - 9 = -5
D. m - 9 = 5 or m + 9 = -5

Answer 1

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

Explanation:

Answer 2

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