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Chapter 2: Q319. (page 184)

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.

4k-k-2鈮�7k-26

Short Answer

Expert verified

k鈮�7

(-鈭�,7]

Step by step solution

01

Step 1. Given information.

The given inequality is

4k-k-2鈮�7k-26

02

Step 2. Solving the inequality.

Distributing and combining like terms:

4k-k+2鈮�7k-26

3k+2鈮�7k-26

Subtracting 7k+2from both sides

3k+2-7k+2鈮�7k-26-7k+2

3k+2-7k-2鈮�7k-26-7k-2

Combining like terms and simplifying

-4k鈮�-28

Diving both sides by -4(this will reverse the inequality as the division is being performed by a negative quantity)

-4k-4鈮�-28-4

Simplifying, the solution to the given inequality becomes

k鈮�7

03

Step 3. Graphing the solution on the number line.

The graph of the solution on the number line is presented below:

04

Step 4. Writing the solution in interval notation.

In interval notation, the solution can be expressed as

(-鈭�,7]

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