Question

1. $\frac{v + 9}{3}=8$ solve for v. a) - 3 b) 15 c) 60 d) 3 25. $6(n + 2)<-72$ a) $n>-14$ b) $n<-10$ c) $n<35/3$ d) $n<-14$ 26. $-2(x + 2)<14$ a) $x<-9$ b) $x<-5$ c) $x>-5$ d) $x>-9$ 27. graph the solution set of the inequality. $-4aleq - 28$ a) graph options b) graph options c) graph options d) graph options 28. graph the solution set of the inequality. $2n + 4<16$ a) graph options b) graph options c) graph options d) graph options

Explanation:

Step1: Solve the equation $\frac{v + 9}{3}=8$ for $v$.

Multiply both sides by 3: $v + 9=8\times3$.

Step2: Simplify the right - hand side and solve for $v$.

$v+9 = 24$, then subtract 9 from both sides: $v=24 - 9$. So $v = 15$.

Step3: Solve the inequality $6(n + 2)<-72$.

First, distribute the 6: $6n+12<-72$. Then subtract 12 from both sides: $6n<-72 - 12=-84$. Divide both sides by 6: $n<-14$.

Step4: Solve the inequality $-2(x + 2)<14$.

Distribute the - 2: $-2x-4<14$. Add 4 to both sides: $-2x<14 + 4 = 18$. Divide both sides by - 2 and reverse the inequality sign: $x>-9$.

Step5: Solve the inequality $-4a\leq - 28$.

Divide both sides by - 4 and reverse the inequality sign: $a\geq7$. A closed - circle is used for $\geq$ on the number line.

Step6: Solve the inequality $2n + 4<16$.

Subtract 4 from both sides: $2n<16 - 4 = 12$. Divide both sides by 2: $n<6$. An open - circle is used for $<$ on the number line.

Answer:

1. b) 15
2. d) $n<-14$
3. d) $x>-9$
4. a) (assuming the graph with a closed - circle at 7 and shading to the right)
5. b) (assuming the graph with an open - circle at 6 and shading to the left)