Luka, Zara, and Kim simplified the following expression: -3(x+4) – 2(5x – 6). Their work is shown below. Who simplified the expression correctly? Explain your answer. (Hint:
None, one, or two of the students could be correct.)
I
Luka
-3(x+4) - 2(5x-6)
-3(x+4) + -2(5x + -6)
-3x + -12 + -10x + 12
-13x
Zara
-3(x+4) - 2(5x-6)
-3x + -12 - (10x -12)
-3x + -12 - 10x + 12
-13x
Kim
-3(x+4) - 2(5x - 6)
-3x + -12 - 10x - 12
-13x - 24

Kim and Zara are correct.

Step-by-step explanation:

Correct simplification:

-3(x+4) - 2(5x-6)

-3x + (-12) - 10x + 12

-3x - 12 - 10x + 12

- 13x

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.