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Chapter 1: Problem 30

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$8 x-2 \geq 14$$

Short Answer

Expert verified
The solution to the inequality \(8x - 2 \geq 14\) is \(x \geq 2\), which in interval notation is represented as \([2, \infty)\). The solution set can be graphed on a number line with a filled dot at 2 and an arrow pointing towards +鈭�.

Step by step solution

01

Solve the inequality

To solve the inequality \(8x - 2 \geq 14\), first, balance the inequality by adding 2 to both sides to isolate the term with x. This results in \(8x \geq 16\). Next, divide both sides by 8 to solve for x, getting the result \(x \geq 2\)
02

Write the solution in interval notation

Interval notation is a way of writing subsets of the real number line. In interval notation, the solution \(x \geq 2\) is represented as \([2, \infty)\). The square bracket [ means the interval includes 2, and the parenthesis ) after 鈭� means it extends indefinitely but doesn't include 鈭� as 鈭� is not a real number.
03

Graph the solution on a number line

To graph the solution on a number line, draw a line and mark out the point corresponding to 2. Since the solution includes 2, place a filled dot at 2. As the solution set extends indefinitely towards +鈭�, draw an arrow starting from 2 and pointing towards the positive direction of the number line.

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