Equivalent Expressions 2

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create two equivalent expressions.

Hint

How does subtracting a number affect the left side of the equation?

Answer

Number of Unique Solutions: 26
1: 2(3x + 4) – 1 = 6x + 7
2: 2(3x + 4) – 7 = 6x + 1
3: 2(3x + 5) – 1 = 6x + 9
4: 2(3x + 5) – 9 = 6x + 1
5: 2(3x + 7) – 5 = 6x + 9
6: 2(3x + 7) – 9 = 6x + 5
7: 2(3x + 8) – 7 = 6x + 9
8: 2(3x + 8) – 9 = 6x + 7
9: 2(4x + 3) – 1 = 8x + 5
10: 2(4x + 3) – 5 = 8x + 1
11: 2(4x + 5) – 1 = 8x + 9
12: 2(4x + 5) – 3 = 8x + 7
13: 2(4x + 5) – 7 = 8x + 3
14: 2(4x + 5) – 9 = 8x + 1
15: 2(4x + 6) – 3 = 8x + 9
16: 2(4x + 6) – 5 = 8x + 7
17: 2(4x + 6) – 7 = 8x + 5
18: 2(4x + 6) – 9 = 8x + 3
19: 2(4x + 7) – 5 = 8x + 9
20: 2(4x + 7) – 9 = 8x + 5
21: 3(2x + 4) – 5 = 6x + 7
22: 3(2x + 4) – 7 = 6x + 5
23: 3(2x + 5) – 7 = 6x + 8
24: 3(2x + 5) – 8 = 6x + 7
25: 4(2x + 3) – 5 = 8x + 7
26: 4(2x + 3) – 7 = 8x + 5

Source: Will Case

5 comments

Mr Kit
April 25, 2019 at 4:19 pm

What I think is really cool about these problems about equivalent expressions is that even though there are multiple answers (and in this case, MANY answers), there are restrictions about where certain numbers can go in the expression – like, all of the samples posted have either a 2 or a 3 in the factor outside of the parentheses.

Ryan Elhasani
June 18, 2021 at 10:55 am

2(3x + 6) – 4 = 6x + 8

Bhargava Gadagottu
June 23, 2021 at 8:11 am

2(4x + 2) – 1 + 8x + 3

Alexis
August 10, 2021 at 11:07 am

2 (3x + 8) – 7 = 6x + 9

Catstar
February 21, 2024 at 11:37 am

2(3x+8)-7+6x+9

Open Middle®

Equivalent Expressions 2

Hint

Answer

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Greatest Common Factor

5 comments

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