Solve the following inequalities:

A) 2w + 17 ˃ - 4w - 25

B) 2.3 + 0.6t ˂ 2 + 0.8t

C) Determine if - 3.5 and 10 make the inequalities in Parts A) and B) true or not. Check both numbers in both inequalities. Show your work.

A) w > - 7

B) 1.5 < t

C) - 3.5 makes A) true and B) false

10 makes both inequalities true

Step-by-step explanation:

The idea of these exercises is to clear our variable, we need it to be alone on one side of the inequality

A) 2w + 17 ˃ - 4w - 25

First, we will put together on one side the terms with a w and on the other the terms without w.

For that, we have to add 4w - 17 on both sides

2w + 17 + 4w - 17 ˃ - 4w - 25 + 4w - 17 (Notice that 17-17=0 and - 4w+4w=0, so we don't have to write them below)

2w + 4w > - 25 - 17

Now we can sum the terms (we didn't do it before because we can't sum a term with a w with one without it)

6w > - 42

We divide by 6 on both sides and we have

6/6w > - 42/6

w > - 7

B) 2.3 + 0.6t ˂ 2 + 0.8t

We start as before; in this case we have to put together the terms with a t (our variable changes name but the idea is the same)

We will add - 2 - 0.6t on both sides

2.3 + 0.6t - 2 - 0.6t ˂ 2 + 0.8t - 2 - 0.6t

2.3 - 2 < 0.8t - 0.6t

Now we sum the terms

0.3 < 0.2t

We divide by 0.2 on both sides and we have

0.3/0.2 < 0.2/0.2t

1.5 < t

C) Let's check - 3.5 on both inequalities:

We have to replace the variable by - 3.5:

2 * (-3.5) + 17 ˃ - 4 * (-3.5) - 25 (remember that if there is no sign between a number and a variable, it means that is a multiplication)

Now we just solve the calculation

-7 + 17 > 14 - 25

10 > - 11

That's true, so - 3.5 makes the inequality true.

Now, in the other inequality, we replace the t by - 3.5 and solve as before

2.3 + 0.6 * (-3.5) ˂ 2 + 0.8 * (-3.5)

2.3 - 2.1 < 2 - 2.8

0.2 < - 0.8

That's false because we are saying that a negative number is bigger than a positive one, so - 3.5 makes the inequality not true.

Now we do the same with 10 in both inequalities:

2*10 + 17 ˃ - 4*10 - 25

20 + 17 > - 40 - 25

37 > - 65

It's true!

2.3 + 0.6*10 ˂ 2 + 0.8*10

2.3 + 6 < 2 + 8

8.3 < 10

It's true!