Question

Determine whether the equation is always, sometimes, or never true.

9. 6(x + 1) = 2(5 + 3x)
10. 3(y + 3) + 5y = 4(2y + 1) + 5

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Answer 1

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Answer:

9. never

10. always

Explanation:

First steps are always removal of parentheses and collecting terms.

The there are identical expressions on either side of the equal sign, the equation is always true.

If the variable coefficients are the same, but the constants are different, the equation is never true.

If the variable coefficients are different, the equation is sometimes true. (true for a specific value of the variable).

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9. 6(x +1) = 2(5 +3x) . . . given

6x +6 = 10 +6x . . . Never true

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10. 3(y +3) +5y = 4(2y +1) +5 . . . given

3y +9 +5y = 8y +4 + 5 . . . eliminate parentheses

8y +9 = 8y +9 . . . Always true