Find the student’s error in solving the following inequality. 31 < –5x + 6
25 < –5x
–5 < x

The student should have added 6 to both sides instead of subtracting it.

The student divided 25/–5 incorrectly.

The student should have switched the direction of the inequality sign to get –5> x for a final answer.

it is the last one. the student should have switched the direction of the inequality.

Step-by-step explanation:

we know product of 2 negative is positive

in the given condition -5 < x. which means that x is greater than -5 so the values of x will be -4, -3, -2 and so forth.

but if this the case then if we take -3 for example and put it in the top equation we get 31 < -5x-3 + 6 = 31<21 this is wrong.

but if it is -5>x this means the value of x is -6,-7,-8 and so forth. if we apply this now for example if we take -8 or -10 and put it in 31 < -5 X -10 + 6 we get 31<56 which is correct. I hope you get the logic.

(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

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step-by-step explanation: