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?

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.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).