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Solve and graph each solution set.2 sf(x) 20, where f(x) = 3x - 1

Solve and graph each solution set.2 sf(x) 20, where f(x) = 3x - 1-example-1
User Masterwok
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1 Answer

11 votes
11 votes

Given the following inequality:


2\leq f(x)\leq20

You know that:


f\mleft(x\mright)=3x-1

Then, you need to rewrite the inequality as follows:


2\leq3x-1\leq20

To solve the inequality, you can follow these steps:

1. Add 1 to all the three parts of the inequality:


\begin{gathered} 2+(1)\leq3x-1+(1)\leq20+(1) \\ 3\leq3x\leq21 \end{gathered}

2. divide all the three parts of the inequality by 3:


\begin{gathered} (3)/(3)\leq(3x)/(3)\leq(21)/(3) \\ \\ 1\leq x\leq7 \end{gathered}

Notice that it can be expressed as a double inequality. This indicates that two inequalities are joined.

Then, to graph the solution on the Number Line, you need to follow the steps shown below:

1. Since both symbols are:


\leq

You can draw to draw a square bracket "[" on the number 1 and another square bracket "]" on the number 7.

2. Draw a line that connects or join the brackets.

Then, you get this graph:

Therefore, the answers are:

- Solution:


1\leq x\leq7

- Graph: Option A.

Solve and graph each solution set.2 sf(x) 20, where f(x) = 3x - 1-example-1
Solve and graph each solution set.2 sf(x) 20, where f(x) = 3x - 1-example-2
User Natsuki
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3.1k points