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.

Question

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Answer 1

To solve the inequality that Inuk wrote, we start with:

\[ 2x - 10 \leq 52 \]

Follow these steps to solve for \( x \):

1. Add 10 to both sides:

\[ 2x - 10 + 10 \leq 52 + 10 \]

This simplifies to:

\[ 2x \leq 62 \]

2. Now, divide both sides by 2:

\[ \frac{2x}{2} \leq \frac{62}{2} \]

This simplifies to:

\[ x \leq 31 \]

The solution to the inequality is:

\[ x \leq 31 \]

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

In interval notation, this result can be expressed as:

\[ (-\infty, 31] \]