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Chapter 6: Problem 43

Solve each inequality and graph the solution set on a number line. \(-x<4\)

Short Answer

Expert verified
The solution to the inequality \(-x < 4\) is \(x > -4\). On the number line, the area to the right of -4 (excluding -4 itself) will be shaded to represent the solution.

Step by step solution

01

Recall Key Rule for Inequalities

Whenever an inequality is multiplied or divided by a negative number, the inequality symbol changes direction. Here the inequality is \(-x < 4\). Multiply both sides of the inequality by -1 to isolate \(x\), but remember to reverse the inequality symbol.
02

Simplify the Inequality

Multiplication of both sides leads to \(x > -4\). This is the inequality solution.
03

Represent Inequality on Number Line

To represent \(x > -4\) on the number line start by marking the number -4 on the number line. As the inequality is not equal to -4, put an open circle at -4. Since it's \(x > -4\), we shade or draw an arrow line to the right side of -4. This illustrates that the solution includes all values greater than -4.

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