Let’s solve each problem step by step. We’ll simplify the left-side expressions and match them to the right-side options.
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1) 2(7n)
Multiply: 2 × 7n =
14n → matches
g
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2) 6(2x - 7)
Distribute: 6×2x = 12x, 6×(-7) = -42 →
12x - 42 → matches
i
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3) (x + 7) - 2
Simplify: x + 7 - 2 =
x + 5 → matches
h
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4) 7x² - 2x + 5 - x
Combine like terms: -2x - x = -3x →
7x² - 3x + 5 → same as
-3x + 5 + 7x² → matches
f
*(Note: Order doesn’t matter in addition — so 7x² - 3x + 5 is same as -3x + 5 + 7x²)*
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5) 9x + 7 - 2 + x
Combine x terms: 9x + x = 10x
Constants: 7 - 2 = 5 →
10x + 5 → matches
b
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6) 10x - 4x + 2 - x
x terms: 10x - 4x = 6x; 6x - x = 5x
Constant: +2 →
5x + 2 → matches
c
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7) 20 - 3x - 7 - 3x
x terms: -3x - 3x = -6x
Constants: 20 - 7 = 13 →
-6x + 13 → matches
a
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8) 4(x + 12)
Distribute: 4×x = 4x, 4×12 = 48 →
4x + 48 → matches
j
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9) 3x + 4 - 2 - 2x
x terms: 3x - 2x = x
Constants: 4 - 2 = 2 →
x + 2 → matches
d
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10) 12y - y + 2y - 4 - 1
y terms: 12y - y = 11y; 11y + 2y = 13y
Constants: -4 -1 = -5 →
13y - 5 → matches
e
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Now let’s list all matches:
1 → g
2 → i
3 → h
4 → f
5 → b
6 → c
7 → a
8 → j
9 → d
10 → e
Final Answer:
1-g, 2-i, 3-h, 4-f, 5-b, 6-c, 7-a, 8-j, 9-d, 10-e
Parent Tip: Review the logic above to help your child master the concept of writing algebraic equations worksheet.
