meredith48034
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1. Suppose you have the inequality 2x < 6. Determine the possible values of x. Explain your reasoning.

2. Michelle is 3 times as old as her sister Beth. For each question, write and solve an equation or inequality to describe Beth's possible ages. Then, graph the solution set on the number line.
a. How old will Beth be when Michelle is at least 27 years old?


b. How old will Beth be when Michelle is younger than 30 years old?

c. How old will Beth be when Michelle is 42 years old?

Answer :

1. Starting with [tex]2x<6[/tex], you can divide both sides by 2 to get [tex]x<3[/tex].

2. We know that [tex]m=3b[/tex], if [tex]m[/tex] and [tex]b[/tex] represent the age of Michelle and Beth, respectively.

2a. If Michelle is at least 27, we have [tex]m\geq 27 \iff 3b\geq 27 \iff b\geq 9[/tex]

2b. If Michelle is younger than 30, we have [tex]m<30 \iff 3b<30 \iff b<10[/tex]

3c. If Michelle is 42, we have [tex]m=42 \iff 3b=42 \iff b=14[/tex]

amna04352

Answer:

1) 2x < 6

Divide both sides by 2

x < 3

x can take any real value less than 3

2) m = 3b

m: Michelle

b: Beth

a) m 》 27

3b 》 27

b 》 9

Beth is atleast 9 years old.

Draw a number line going towards right from 9, with a closed circle at 9 because it's included

b) m < 30

3b < 30

b < 10

Number line going towards left from 10 with an open circle at 10.

c) m = 42

3b = 42

b = 14

On the number line, just a closed circle at 14.

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