Question

Tell whether x=6 is a solution of x−1 ≤ 7.

Answer 1

x = 6 is a solution of x - 1
`\leq` 7.

Explanation:

First, plug in x = 6 into the inequality.

x - 1
`\leq` 7 for x = 6

6 - 1
`\leq` 7

Now, solve.

6 - 1 = 5

5
`\leq` 7

The statement above is true, so x = 6 is a solution to x - 1
`\leq` 7.

Please inform me of any mistakes.

Answer 2

Answer: Yes.

Explanation:

We will substitute the given solution for x into the inequality and see if the inequality remains true.

Given:

x - 1 ≤ 7

Substitute known values:

6 - 1 ≤ 7

Subtract:

5 ≤ 7 ✓

Since 5 is less than 7, yes, x = 6 is a solution.

We can also solve the inequality for x.

Given:

x - 1 ≤ 7

Add 1 from both sides of the inequality:

x ≤ 8

This shows that any x-value less than or equal to 8 will be a solution.