Algebra is not epic or i just don't know how to do it, and in a state of angered ignorance i have come here to seek

Choice (D): x<=-2 or x>=8

Explanation:

An absolute value |x| is a function that has a "tricky" definition: it equals x is x >=0, but changes abruptly to -x for values of x<0.  

This two-case scenario has to be respected and built into a solution of any equation or inequality involving absolute values.

So we start treating the inequality for two cases:

(1) for the case when x-3 >=0, fo which the absolute value is the same what is inside the vertical brackets:

(2) for the other case of x-3<0, in which case we need that extra minus sign:

So putting both cases together, the solution to the inqueality is an x falling to either of the two intervals: x>=8 or x<=-2, which corresponds to choice (D).

their is no graph showing

step-by-step explanation:

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.