Problem 59 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: Write down the inequality

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

Step 2: 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: $$ -y \leq 9 $$

Step 3: 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: $$ y \geq -9 $$

Step 4: 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.

Key Concepts

Algebraic Inequalities

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