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Chapter 6: Problem 30

Solve each inequality and graph the solution set on a number line. \(\frac{x}{4}<-1\)

Short Answer

Expert verified
The solution to the inequality \(\frac{x}{4} < -1\) is \(x < -4\). On a number line, this is represented as a shaded line extending from -4 (excluding -4) to left, towards negative infinity.

Step by step solution

01

Isolate the variable

In this step, we must isolate x by multiplying both sides of the inequality by 4. So we get \(x < -4\)
02

Graph the solution on a number line

Now, we must visualize the solution on a number line. Number -4 is an open circle on the line because the inequality is '<', not '鈮�'. Everything to the left of -4, excluding -4 itself, is part of the solution. So we shade the line to the left of -4 (negative infinity to -4).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The fastest way for me to solve \(x^{2}-x-2=0\) is to use the quadratic formula.

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Describe ways in which solving a linear inequality is different than solving a linear equation.

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