Applications of Inequalities Practice

Question

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Question
Ten less than twice a number is equal to at most 52. What are all the possible values of the number? Inuk wrote the inequality 2x−10≤52
, where x
equals the number, to help solve this problem. Solve his inequality. Use the letter x
as your variable and write your x
term first.

Answer 1

To solve the inequality \(2x - 10 \leq 52\), we can follow these steps:

1. Add 10 to both sides to isolate the term with \(x\): \[ 2x - 10 + 10 \leq 52 + 10 \] This simplifies to: \[ 2x \leq 62 \]

2. Divide both sides by 2 to solve for \(x\): \[ \frac{2x}{2} \leq \frac{62}{2} \] This simplifies to: \[ x \leq 31 \]

Thus, the solution to the inequality is: \[ x \leq 31 \]

This means that all possible values of the number \(x\) are those numbers that are less than or equal to 31.