Algebra 2 homework help?

Question

Solve the inequality for x and use interval notation: 2x – 3 > 5
(-∞ , 4)
(-∞ , 4]
[4, ∞ )
(4, ∞ )


Solve the inequality for x and use interval notation: -4 + x < -3 – 2x
(-∞ , (1/3))
(-∞ , (1/3)]
[(1/3), ∞ )
((1/3), ∞ )


Solve the inequality for x and use interval notation: (2/3)x – (4/3) ≥ (1/4)
(-∞ , (19/8))
(-∞ , (19/8)]
[(19/8), ∞ )
((19/8), ∞ )


Solve the inequality for x: 4 < x – 5 ≤ 6
9 < x ≤ 11
9 ≤ x < 11
-1 < x ≤ 1
-1 ≤ x < 1


Solve the inequality for x: 2 ≤ -5x – 13 < 7
3 ≤ x < 4
3 < x ≤ 4
-4 ≤ x < -3
-4 < x ≤ -3


Solve the inequality for x and graph: -8 < -2x – 1 ≤ -5. Your graph contains _______.
"[" on 2, and "]" on (7/2)
"[" on 2, ")" on (7/2)
"(" on 2, ")" on (7/2)
"(" on 2, "]" on (7/2)

Answer 1

i'll help you on the first couple of steps for each equation:

2x-3>5

add 3 to both sides:

2x>8



-4 + x < -3 – 2x

add 2x to both sides:

-4+3x<-3

add 4 to both sides:

3x<1



(2/3)x – (4/3) ≥ (1/4)

multiply the equation by 12:

8x-16≥3

add 16 to both sides:

8x≥19



4 < x – 5 ≤ 6

add 5 to all sides:

9 < x ≤ 11


2 ≤ -5x – 13 < 7

add 13 to all sides:

15≤-5x<20

divide all sides by -5 and flip the sign:

-3 ≥ x > -4



-8 < -2x – 1 ≤ -5

add 1 to all sides:

-7<-2x≤-4

divide all sides by -2 and flip the signs:

(7/2) > x ≥ 2

"[" on 2, ")" on (7/2)

remember that "[" or "]" is for ''≤'' or ''≥'' and "(" or ")" is for "<'' or ''>''