Solve the inequality, then identify the graph of the
solution.
2x-1> x + 2

x > 3

Solution:

The given inequality is 2x – 1 > x + 2.

To simplify the inequality 2x – 1 > x + 2.

2x – 1 > x + 2

Subtract x on both sides of the expression.

⇒ 2x – 1 – x > x + 2 – x

⇒ 2x – x – 1 > x – x + 2

⇒ x – 1 > 2

Add 1 on both sides of the expression.

⇒ x – 1 + 1 > 2 + 1

⇒ x > 3

The graph of the solution x > 3 is attached below.

(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