Question

10 joel is 4 years less than one - third the age of his coach. if the coach is n years old, which expression describes joels age? a. $\frac{n}{3}-4$ b. $3n - 4$ c. $\frac{n - 4}{3}$ d. $4-\frac{n}{3}$ 11 which description best matches the interval $4,infty)$? a. closed circle at 4 with shading to the right b. open circle at 4 with shading to the right c. closed circle at 4 with shading to the left d. open circle at 4 with shading to the left 12 a number line shows an open circle at - 5 and a closed circle at 7 with shading between. which interval matches this graph? a. $(-5,7$ b. $-5,7)$ c. $-5,7$ d. $(-5,7)$ 13 directions: select all correct answers. identify all possible solutions to the compound inequality $2<3x - 1<17$. a. $(1,6)$ b. ${x|1

Explanation:

Step1: Analyze Joel's age problem

One - third of the coach's age is $\frac{n}{3}$, and 4 years less than that is $\frac{n}{3}-4$.

Step2: Analyze interval notation for [4, $\infty$)

A closed - bracket means a closed circle, and $\infty$ means shading to the right. So it's a closed circle at 4 with shading to the right.

Step3: Analyze number line graph for open circle at - 5 and closed circle at 7

An open circle means the endpoint is not included (parenthesis), and a closed circle means the endpoint is included (bracket), so the interval is (-5, 7].

Step4: Solve the compound inequality $2 < 3x - 1 < 17$

Add 1 to all parts: $2+1<3x - 1+1<17 + 1$, which gives $3<3x<18$. Divide all parts by 3: $1 < x<6$, which can be written as the interval (1, 6) or $\{x|1 < x<6\}$.

Step5: Match verbal to algebraic expressions

1. The product of 3 and $x$ is $3x$, and twelve less than that is $3x - 12$.
2. The difference of a number $y$ and 12 is $y - 12$.
3. One - half of $x$ is $\frac{x}{2}$, and subtracted from 12 is $12-\frac{x}{2}$.
4. Five times a number $k$ is $5k$, and four more than that is $5k + 4$.

Answer:

[10] A. $\frac{n}{3}-4$
[11] B. Closed circle at 4 with shading to the right
[12] A. (-5, 7]
[13] A. (1, 6), B. $\{x|1 < x<6\}$
[14]

1. C. $3x - 12$
2. D. $y - 12$
3. A. $12-(x/2)$
4. B. $5k + 4$