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Chapter 7: Problem 17

Graph each linear inequality. \(x \leq 2\)

Short Answer

Expert verified
The graph of the linear inequality \(x \leq 2\) is a line that extends from 2 to the left side of the number line, including 2 itself.

Step by step solution

01

Understand the inequality

In the inequality \(x \leq 2\), it means x can be any number less than or equal to 2.
02

Draw the number line

Start by drawing a number line. Mark the number 2 on this line, as this is the key number in our inequality.
03

Mark the point

On number '2' on your number line, draw a closed circle to represent that x can be equal to 2.
04

Draw the line segment

Now, considering that x can be any number less than 2, draw a line extending from 2 to the left side of the number line.
05

Wrap up

The completed graph represents all values of x which satisfy the condition \(x \leq 2\).

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Without graphing, in Exercises 64-67, determine if each system has no solution or infinitely many solutions. \(\left\\{\begin{array}{l}3 x+y<9 \\ 3 x+y>9\end{array}\right.\)

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