What is the reason for each step in the solution of the inequality? 4(x+6)>−5(x+5)−14 Select the reason for each step from th

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3 years ago

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What is the reason for each step in the solution of the inequality? 4(x+6)>−5(x+5)−14 Select the reason for each step from th

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4(x+6)>−5(x+5)−14 Given
4x+24>−5x−25−14 choose
4x+24>−5x−39 choose
4x+63>−5x Addition Property of Order
63>−9x Subtraction Property of Order
−7<x choose

Mathematics

2 answers:

Nesterboy [21] · Answer 1 · 2021-12-03T16:22:33+03:00

Hey there!!

The equation given :

4 ( x + 6 ) > -5 ( x + 5 ) - 14

... 4x + 24 > -5x - 25 - 14

... 4x + 24 > - 5x - 39

Add 39 on both sides

... 4x + 63 > - 5x

Subtract 4x on both sides

... 63 > - 9x

Divide by -9 on both sides

When we divide both sides by a negative number, we switch the signs.

... -7 < x

Hope my answer helps!!

Serhud [2] · Answer 2 · 2021-12-03T18:20:29+03:00

4(x + 6) > −5(x + 5) − 14 Given

(4)(x) + (4)(6) > (-5)(x) + (-5)(5) - 14

4x + 24 > −5x − 25 − 14 Distributive property

4x + 24 > -5x - (25 + 14)

4x + 24 > −5x − 39 Simplify right side

4x + 24 + 39 > -5x -39 + 39

4x + 63 > −5x Addition property of equality

4x - 4x + 63 > -5x - 4x

63 > −9x Subtraction property of equality

63 : (-9) < -9x : (-9) /-9 < 0 → switch the signs/

−7 < x Division property of equality