The variable z is directly proportional to x. when x is 11, z has the value 44. what is the value of z when x = 21?

Directly proportional, both increase/decrease, Multiple k(constant you needed to solve for)..

Inversely --one increases as the other decreases, increase the denominator & fraction gets smaller So

Problem:

Dirextly to X (× by X)

Inversely to Y, (÷ by Y)

Z= k X/Y

Solve, working backwards: Z =5 becomes

5 = k (X) ÷ (Y). And

X=15 and Y =9 becomes

5= k(15)/(9). Undo ÷9, ×9 both sides

45= k(15). Now undo ×15 by ÷15 both sides

45/15 = 3. So k=3, (also called your constant of variation)and your Equation/Proportion becomes...

Z = 3X/Y

Use the new #s X=23, Y=14

Z= 3×23÷14 = 69/14. If they want spirochete answer divide and round to corresponding # if decimals

b, i believe, but not sure.

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.