Pre-Algebra Worksheets | Algebraic Expressions Worksheets - Free Printable

Let's solve each problem one by one by substituting the given value of the variable into the equation and checking whether the equation is true or false.

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1. $ y + 15 = 30 $, $ y = 20 $

Substitute:
$ 20 + 15 = 35 $
But $ 35 \neq 30 $ → False

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2. $ 9x = 63 $, $ x = 7 $

Substitute:
$ 9 \times 7 = 63 $ → $ 63 = 63 $ → True

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3. $ n \div 12 = 36 $, $ n = 108 $

Substitute:
$ 108 \div 12 = 9 $
But $ 9 \neq 36 $ → False

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4. $ s - 62 = 44 $, $ s = 106 $

Substitute:
$ 106 - 62 = 44 $ → $ 44 = 44 $ → True

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5. $ 32 \times y = 256 $, $ y = 8 $

Substitute:
$ 32 \times 8 = 256 $ → $ 256 = 256 $ → True

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6. $ n + 65 = 87 $, $ n = 27 $

Substitute:
$ 27 + 65 = 92 $
But $ 92 \neq 87 $ → False

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7. $ 64 = 8m $, $ m = 8 $

Substitute:
$ 8 \times 8 = 64 $ → $ 64 = 64 $ → True

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8. $ 56 + t = 72 $, $ t = 26 $

Substitute:
$ 56 + 26 = 82 $
But $ 82 \neq 72 $ → False

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9. $ x - 63 = 37 $, $ x = 100 $

Substitute:
$ 100 - 63 = 37 $ → $ 37 = 37 $ → True

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10. $ n + 42 = 77 $, $ m = 45 $

Wait — the equation has n, but the given value is for m. That’s a mismatch.

The equation is: $ n + 42 = 77 $, and we're told $ m = 45 $. But m does not appear in the equation.

So unless there's a typo, this is invalid. But since the question asks us to evaluate based on the given variable, and m is not in the equation, we cannot determine if it's true or false using that value.

But likely, it's a typo — perhaps they meant $ n = 45 $? Let's check:

If $ n = 45 $, then $ 45 + 42 = 87 \neq 77 $ → False

But the given value is $ m = 45 $, which doesn't help.

Alternatively, maybe it's supposed to be $ m + 42 = 77 $, and $ m = 45 $? Then:

$ 45 + 42 = 87 \neq 77 $ → False

But as written: $ n + 42 = 77 $, $ m = 45 $ → The variable m is irrelevant here.

So unless there's a typo, we can't evaluate this statement.

But assuming it's a typo and they meant $ n = 45 $, then:

$ 45 + 42 = 87 \neq 77 $ → False

Alternatively, if they meant $ m = 35 $, then $ 35 + 42 = 77 $ → True

But with $ m = 45 $, and no use of $ m $, it's not valid.

However, since the instruction says "for the given value of each variable", and $ m $ is not in the equation, the only logical conclusion is that the statement cannot be evaluated — but since it's a true/false question, likely it's a typo.

Given the pattern, probably it should be: $ n + 42 = 77 $, $ n = 45 $ → then $ 45 + 42 = 87 \neq 77 $ → False

Or possibly: $ m + 42 = 77 $, $ m = 45 $? Then $ 45 + 42 = 87 \neq 77 $ → False

Either way, it's False.

But strictly speaking, if the equation is $ n + 42 = 77 $, and $ m = 45 $, then we don’t have enough info — but since $ m $ isn't used, and the equation involves $ n $, and $ n $'s value isn't given, we cannot evaluate.

But that seems unlikely — so most likely, it's a typo and should be $ n = 45 $. Then:

$ 45 + 42 = 87 \neq 77 $ → False

So we’ll go with False, assuming a typo.

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Final Answers:

1. False
2. True
3. False
4. True
5. True
6. False
7. True
8. False
9. True
10. False (assuming typo, $ n = 45 $)

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✔ Answer Key:

1. False
2. True
3. False
4. True
5. True
6. False
7. True
8. False
9. True
10. False