Marcie solved the following inequality, and her work is shown below:

−2(x − 5) − 12 ≤ 4 + 6(x + 3)
−2x + 10 − 12 ≤ 4 + 6x + 18
−2x − 2 ≤ 6x + 22
−8x ≤ 24
x ≤ −3

what mistake did marcie make in solving the inequality?

she subtracted 6x from both sides when she should have added 2x.
she added 2 to both sides when she should have subtracted 22.
when dividing by −8, she did not change the ≤ to ≥.
she did not make a mistake.

When dividing by −8, she did not change the ≤ to ≥

Step-by-step explanation:

Marcie solved the following inequality

-2 and 6 is distributed inside the parenthesis and did it correctly

Like terms are combined and it is correct.

Like terms are combined further

When we divide or multiply an inequality by a negative number then we change the inequality sign.

When dividing by −8, she did not change the ≤ to ≥

answer: 5

step-by-step explanation:

since, the range is the difference between the lowest and highest values of the given sample space.

and, here the sample space = { 3, 1, 0, 4, 1, 4, 2, 3, 0, 5, 0, 1, 1, 2, 0, 4, 1,4, 4 ,2 ,3 ,2 ,0 ,1 ,4 }

here, the highest value of the given sample = 5

and, the lowest value = 0

therefore, the range of the sample space = 5 - 0 = 5

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus