Algebra

Question 1

x + 2y = 8

x - 2y = 4

Answer 1

x + 2y = 8
x - 2y = 4   add
--------------------
2x = 12
x = 6   answer for x

x + 2y = 8 substitute to get answer for x
6 + 2y = 8
2y = 2
y = 1

Question 2

3x - 2x + 7y

Solve for if x = -3 and y = 7

Answer 2

(-3 x 3) - (-3 x 2) + (7 x 7)
-9 - -6 + 49
-9 + 6 + 49
-3 + 49
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46

Question 3

If z ≥ 3, what are the possible values of z?

Answer 3

3, 4, 5, 6, 7, 8, …

z is greater than or equal to 3, so it can be 3 and any number greater than 3.

Question 4

Simplify:

3x + 5 + x2 - 2x + 2x2 - 1

Answer 4

Rearrange the expression so that like terms are next to each other:
x2 + 2x2 + 3x - 2x + 5 - 1

And then simplify:
3x2 + x + 4

Question 5

Is x the same as x^2?

Answer 5

x is not the same as x2, so they cannot be added together.

Question 6

The formula for the volume (V) of a sphere is:
V = 4/3 π r3
Rearrange the formula to make ‘r’ the subject.

Answer 6

V = 4/3 π r 3
Multiply both sides by 3.
3V = 4πr3
Divide by 4π.
= 3V over 4π = r to the power of 3
Take the cube root of both sides.
cube root 3V over 4π = r
Or r = cube root 3V over 4π