Answer:
2. B) n > 2
4. B) -3
5. C) 1[tex]\frac{1}{2}[/tex] (Which is equal to 1.5)
8. D) x > [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
2. -6n < -12
To solve for n, divide by -6. When divide by a negative, you flip the sign.
n > 2
4. 2(n + 5) [tex]\geq[/tex] 4 and 3(n - 1) < 3
Divide by 2 for the first inequality and divide by 3 for the second inequality.
n + 5 [tex]\geq[/tex] 2 and n - 1 < 1
Now subtract 5 and add 1
n [tex]\geq[/tex] -3 and n < 2
Since the inequality says and, both equations have to be true when n is plugged in. We can see that -3 works, since it is equal to -3 AND is less than 2.
5. 4x - 7 [tex]\geq[/tex] [tex]\frac{-12x+14}4}[/tex]
Multiply by 4 to both sides
16x - 28 [tex]\geq[/tex] -12x + 14
Now add 12x and add 28.
28x [tex]\geq[/tex] 42
Divide by 28 to get x.
x [tex]\geq[/tex] 1.5
So the answer is C.
8. 3(2x - 1) > 4x - 2
For this one, distribute the 3 to the numbers in the parentheses.
6x - 3 > 4x - 2
Add 3 and subtract 4x.
2x > 1
Divide by 2.
x > [tex]\frac{1}{2}[/tex]
