In the following activity, match each pair of equivalent expressions. 1. 3(x + 5) -3x + 6 + 4x 2. (x + 14) - (8 - 2x) -7 + 6x -

Question

3 years ago

5

In the following activity, match each pair of equivalent expressions. 1. 3(x + 5) -3x + 6 + 4x 2. (x + 14) - (8 - 2x) -7 + 6x -

4x + 3 3. (7 + 5x) + (-4x - 1) 9x - 2(3x - 3) 4. -4(x + 1) + 5x -2x + 9 + 5x + 6 5. 2(x - 2) (7 - 2x) + (3x - 11)
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Mathematics

2 answers:

Jet001 [13] · Answer 1 · 2022-01-18T20:20:22+03:00

Jet001 [13]3 years ago

6 0

1. 3(x + 5), matches -2x + 9 + 5x + 62. (x + 14) - (8 - 2x), matches 9x - 2(3x - 3)3. (7 + 5x) + (-4x - 1), matches -3x + 6 + 4x4. -4(x + 1) + 5x, matches (7 - 2x) + (3x - 11)5. 2(x - 2), matches -7 + 6x - 4x + 3

Fittoniya [83] · Answer 2 · 2022-01-18T21:34:49+03:00

1. 3(x + 5), matches -2x + 9 + 5x + 6
2. (x + 14) - (8 - 2x), matches 9x - 2(3x - 3)
3. (7 + 5x) + (-4x - 1), matches -3x + 6 + 4x
4. -4(x + 1) + 5x, matches (7 - 2x) + (3x - 11)
5. 2(x - 2), matches -7 + 6x - 4x + 3

In this problem, you have a total of 10 equations. The formatting on this problem is extremely poor, but I'm assuming that there's 2 columns of equations and that for the 1st equation in each column, you need to match against an equation in the 2nd column that has the same value. So what you need to do is expand and simplify all 10 equations and see which pairs match up. So, first off, we need to actually determine the 10 equations (hint: line breaks and white space make things MUCH easier and I wouldn't have to do so much guess work in order to actually figure out what the problem is never-mind the actual solution to the problem). My best guess as to the separate equations is:
First column
1. 3(x + 5)
2. (x + 14) - (8 - 2x)
3. (7 + 5x) + (-4x - 1)
4. -4(x + 1) + 5x
5. 2(x - 2)

Second column
1. -3x + 6 + 4x
2. -7 + 6x - 4x + 3
3. 9x - 2(3x - 3)
4. -2x + 9 + 5x + 6
5. (7 - 2x) + (3x - 11)

Solution:
First, simplify all 10 equations.
1. 3(x + 5) = 3x + 15
2. (x + 14) - (8 - 2x) = x + 14 - 8 + 2x = 3x + 6
3. (7 + 5x) + (-4x - 1) = 7 + 5x - 4x - 1 = x + 6
4. -4(x + 1) + 5x = -4x - 4 + 5x = x - 4
5. 2(x - 2) = 2x - 4

Second column
1. -3x + 6 + 4x = x + 6
2. -7 + 6x - 4x + 3 = 2x - 4
3. 9x - 2(3x - 3) = 9x - 6x + 6 = 3x + 6
4. -2x + 9 + 5x + 6 = 3x + 15
5. (7 - 2x) + (3x - 11) = 7 - 2x + 3x - 11 = x - 4

Now that we have all 10 equations simplified, we can simply match them together.
1. 3(x + 5), matches -2x + 9 + 5x + 6
2. (x + 14) - (8 - 2x), matches 9x - 2(3x - 3)
3. (7 + 5x) + (-4x - 1), matches -3x + 6 + 4x
4. -4(x + 1) + 5x, matches (7 - 2x) + (3x - 11)
5. 2(x - 2), matches -7 + 6x - 4x + 3