Answer:
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 <u>we can't sum a term with a w with one without it</u>)
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!
