Complete the logical argument by giving a reason for each step.
1. 5(2x - 1) = 9x + 2
10x - 5 = 9x + 2
10x = 9x + 7
x=7
given
a. ?
b.?
c.?

A = Distributive Property of Multiplication

B = Addition Property of Equality

C = Subtraction Property of Equality

Step-by-step explanation:

Given:

5(2x - 1) = 9x + 2

The first step is to use the distributive property and multiply 5 to both numbers inside the brackets. So, A will be Distributive property of multiplication, which will result in:

5(2x) - 5(1) = 9x + 2

10x - 5 = 9x + 2

The next step is to add 5 on both sides of the equation. So, B will be the Addition property of equality, which will result in:

10x - 5 + 5 = 9x + 2 + 5

10x = 9x + 7

The next step is to subtract 9x from both sides of the equation. So, C will be the Subtraction property of Equality, which will result in:

10x - 9x = 9x + 7 - 9x

x = 7

2 x t divided by n

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240