Question

Having a hard time with this question... Can anybody help?

Which value satisfies the inequality 5x + 7 ≤ 8x - 3 + 2x?
A) -2
B) -1
C) 0
D) 2

Answer 1

D) 2

Explanation:

`5x+7\leq8x-3+2x\qquad\text{combine like terms}\\\\5x+7\leq(8x+2x)-3\\\\5x+7\leq10x-3\qquad\text{subtract 7 from both sides}\\\\5x\leq10x-10\qquad\text{subtract}\ 10x\ \text{from both sides}\\\\-5x\leq-10\qquad\text{change the signs}\\\\5x\geq10\qquad\text{divide both sides by 5}\\\\x\geq2\\\\Answer:\ x=2,\ \text{because}\ 2\geq2,\ (\geq-\text{greater than or equal to}),\ \text{2 is equal to 2}.`

Answer 2

I'd just run through the numbers.

A. 5(-2) + 7 vs. 8(-2) - 3 + 2(-2)
-3 is less than or equal to -23 which is not true so A is wrong

B. 5(-1) + 7 vs. 8(-1) - 3 + 2(-1)
2 is less than or equal to -13 which is also wrong

C. 5(0) + 7 vs 8(0) - 3 + 2(0)
7 is less than or equal to -3 which is still wrong.

so you could assume d but just to be sure...

D. 5(2) + 7 vs 8(2) - 3 + 2(2)
17 is less than or equal to 17 which is true.

so D is right.