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Chapter 2: Q 422. (page 196)

Solve the given inequality, graph the solution on the number line, and write the solution in interval notation.4x-2>6and3x-1鈮�-2.

Short Answer

Expert verified

The solution of inequality isx>2or localid="1644232172620" x鈮�-13. The interval notation is(-鈭�,-13]鈭�(2,鈭�), and the figure is given below:

Step by step solution

01

Step 1. Given information.

We have given inequality:

4x-2>6

3x-1鈮�-2

02

Step 2. Solve the first inequality.

First inequality:

4x-2>鈥�6

Add 2 to both sides:

4x-2+2>6+24x>8

Divide both sides by4:

4x4>84x>2

Interval notation:2,鈥�鈭�鈥�

03

Step3. Solve the second inequality.

Second inequality:

3x-1鈮�鈥�-2

Add 1to both sides:

3x-1+1鈮�鈥�-2+13x鈮�鈥�-13x3鈮�-13x鈮�鈥�-13

Interval notation:鈥�(-鈭�鈥�,鈥�-13]

04

Step 4. Draw the solution the number line.

We have the solution:

x>2or

x鈮�-13

Draw on the number line:

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