Question

What is the justification for each step in the solution of the equation?

13x−4=−9(4+3x)+12

Select from the drop-down menus to correctly justify each step.


13x−4=−9(4+3x)+12 Given
13x−4=−36−27x+12
13x−4=−24−27x
40x−4=−24 Addition Property of Equality
40x=−20
x=−12 Division Property of Equality

Answer 1

13x−4=−36−27x+12: Distributive property

13x−4=−24−27x: Combine like terms

40x=−20: Addition Property of equality

Answer 2

13x−4=−9(4+3x)+12 Given
13x−4=−36−27x+12 distributive property [-9 (4 + 3x) + 12 = -36 -27x]
13x−4=−24−27x Subtraction property [ -36 + 12 ] = -24
13x + 27x = -24 + 4 collecting like terms
40x=−20 Addition Property of Equality
as 13x + 27 x = 40x and -24 + 4 = -20
x=−1/2 Division Property of Equality
40x / 40 = x and 20 /40 = 1/2