Explain the Error Find the error in the solution, and then solve it correctly.

7x + 21 + 6x = 4

7x + 21 = -2

7x = -23

-23

7

(select) was subtracted from the left side, but (select) was subtracted from the right side. The

Subtraction Property of Equality states that you can subtract the same number from each side and the

equation will remain true. But 6x and 6 are not the same number (unless x is (select)).

X =

Step-by-step explanation:

7x+21+6x=4 combine terms

13x+21=4  subtract 21 from both sides

13x= -17 divide by 13

x= -17/13

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

(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