We are asked to determine if a statement is true. Let's start by looking at the individual expressions. The numbers for which $∣ a ∣ > 7$ are the ones that are further away from $0$ than $7 .$ Let's illustrate this on a number line.

Since $a + 3 = a - (- 3),$ the numbers for which $∣ a + 3 ∣ > 10$ are the ones that are further away from $- 3$ than $10 .$ Let's illustrate this on a number line, too.

Can the Statement be True?

We can see that there are common numbers in the two solution sets, so the statement can be true. For example, the statement is true for

a = 10 .

∣ 10 ∣ = 10 > 7, and ∣ 10 + 3 ∣ = ∣ 13 ∣ = 13 > 10

Can the Statement be Not True?

However, there are also numbers in the first solution set which are not in the second. This means that there are counterexamples to the statement. For example, the statement is not true for

a = - 10 .

∣ - 10 ∣ = 10 > 7, but ∣ - 10 + 3 ∣ = ∣ - 7 ∣ = 7 ≯ 10

Conclusion

This means the statement is sometimes true.

Extra

Is the converse true?

Note, since all numbers of the second solution set are also in the first, the converse of the statement is always tue.

If ∣ a + 3 ∣ > 10, then ∣ a ∣ > 7

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