Question

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 the drop-down menus.
​ 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

Answer 1

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!!

Answer 2

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