Question

ii. solve each inequality and graph its solution.

1. 4(6x - 4) > - 160

24x-16 > - 160
+16 + 16
24x > - 144
\frac{24x}{24}>\frac{- 144}{24}
x > - 6

1. 4(5m - 2) < - 128

20m - 8 < - 128
+8 + 8
20m < - 120
\frac{20m}{20}<\frac{- 120}{20}
m < - 6

1. - 5(5n - 8) ≤ 140

• 25n+40 ≤ 140

+40 + 40

1. 3a + 2(4a - 7) ≤ - 91

Explanation:

Step1: Expand the left - hand side

For $4(6x - 4)>-160$, we get $24x-16 > - 160$; for $4(5m - 2)<-128$, we get $20m-8 < - 128$; for $-5(5n - 8)\leq140$, we get $-25n + 40\leq140$; for $3a+2(4a - 7)\leq - 91$, we get $3a + 8a-14\leq - 91$.

Step2: Isolate the term with the variable

For $24x-16 > - 160$, add 16 to both sides: $24x>-144$. For $20m - 8 < - 128$, add 8 to both sides: $20m<-120$. For $-25n + 40\leq140$, subtract 40 from both sides: $-25n\leq100$. For $3a + 8a-14\leq - 91$, combine like - terms to get $11a-14\leq - 91$, then add 14 to both sides: $11a\leq - 77$.

Step3: Solve for the variable

For $24x>-144$, divide both sides by 24: $x > - 6$. For $20m<-120$, divide both sides by 20: $m < - 6$. For $-25n\leq100$, divide both sides by - 25 and reverse the inequality sign: $n\geq - 4$. For $11a\leq - 77$, divide both sides by 11: $a\leq - 7$.

Answer:

1. Solution: $x > - 6$. Graph: Open circle at $x=-6$ and a line extending to the right.
2. Solution: $m < - 6$. Graph: Open circle at $m = - 6$ and a line extending to the left.
3. Solution: $n\geq - 4$. Graph: Closed circle at $n=-4$ and a line extending to the right.
4. Solution: $a\leq - 7$. Graph: Closed circle at $a=-7$ and a line extending to the left.