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Chapter 5: Problem 59

For the following problems, solve the inequalities. $$ 5-y \leq 14 $$

Short Answer

Expert verified
Question: Solve the inequality and find the range of values for y: 5 - y 鈮� 14. Answer: The solution of the inequality is y 鈮� -9. This means that any value of y greater than or equal to -9 will satisfy the inequality.

Step by step solution

01

Write down the inequality

The given inequality is: $$ 5 - y \leq 14 $$
02

Isolate y

In order to isolate y, we will first move the constant term to the other side of the inequality sign. To do this, we will subtract 5 from both sides: $$ 5 - y - 5 \leq 14 - 5 $$ This simplifies to: $$ -y \leq 9 $$
03

Divide by -1

To get y by itself, we now need to divide both sides of the inequality by -1. It is important to remember that when we divide or multiply an inequality by a negative number, the inequality sign changes direction. Hence, we get: $$ y \geq -9 $$
04

Write down the solution

We now have the solution of the inequality: $$ y \geq -9 $$ This means that any value of y greater than or equal to -9 will satisfy the inequality.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Algebraic Inequalities
Algebraic inequalities are similar to equations but instead of an equal sign, they involve comparison operators such as <, >, Turn on the

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