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24 September, 13:27

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.

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  1. 24 September, 14:34
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    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!
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