Question

EASY POINTS AND PLEASE HELP ASAP!!! WILL MARK BRAINLIST! ;)
1. Justify each step in solving the equation -2(3x+7)=32-4x by writing a reason for each statement.

* Picture down below applies to this question. All I need help with is putting in the reasons for each step.

2. Write the equation of the line perpendicular to 4x+y=3 that passes through (-4,-6). Write your answer in slope-intercept form. Show your work.

Answer 1

Step-by-step explanation:

1.

$- 2(3x + 7) = 32 - 4x \\ distribute \\ - 2 \times 3x = - 6x \\ - 2 \times 7 = - 14 \\ - 6x - 14 = 32 - 4x \\ add \: 4x \: to \: both \: sides \\ - 6x + 4x = 32 - 4x + 4x \\ - 2x = 32 \\ divide \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{32}{ - 2} \\ \\ x = - 16$

2.

$4x + y = 3 \\ y = - 4x + 3 \\ using \: point \: slope \: form \\ y - y1 = m(x - x1) \\ y + 6 = - 4(x + 4) \\ y + 6 = - 4x - 16 \\ y = - 4x - 22$

First equation: Your equation is given.

Second equation: Distribute by multiplying every number in the parentheses by the number outside it.

3rd equation: Combine like terms by adding 4x to both sides.

4th equation: Combine like terms by subtracting 14 from both sides.

5th equation: Divide both sides by -2, the coefficient of x.