The equations that are equivalent to (5x + 6)2 = 3-(4x +12) is (5x+6)2=−4x−9.
Option B is correct.
The very first thing to do is to solve the expression in the given question.
SO,
(5x + 6)2 = 3-(4x +12)
Open brackets
- 10x + 12 = 3 - 4x - 12
- 10x + 12 = -4x - 9
Collect like terms
- 10x + 4x = -9 - 12
- 14x = -21
x = -21/14
Now, we will solve each of the given options to determine which one corresponds to the solution to the expression above.
Starting with Option (a)
5x + 6 = 3 - (4x + 12)
Open brackets
- 5x + 6 = 3 - 4x - 12
- 5x + 6 = -4x - 9
- 5x + 4x = -9 - 6
- 9x = -15
- x = -15/9
Option (a) is incorrect
b.
(5x + 6 )2 = -4x - 9
Open brackets
- 10x + 12 = -4x -9
- Collect like terms
- 10x + 4x = -12 -9
- 14x = -21
- x = -21/14
Option (b) is correct
(c.)
52x + 3 = 3 - (4x + 12)
Open brackets
- 52x + 3 = 3 - 4x - 12
- 52x + 3 = -4x - 9
- 52x + 4x = -9 - 3
- 56x = - 12
- x = -12/56
- x = -3/14
Option (c) is incorrect
(d)
(5x + 6)2 = -4x + 15
Open brackets
- 10x + 12 = -4x + 15
- 10x + 4x = -12 + 15
- 14x = 3
- x = 3/14
Option (d) is incorrect
(e)
5x + 6 = -8x - 18
Collect like terms
- 5x + 8x = -18 - 6
- 13x = - 24
- x = -24/13
Option (e) is incorrect
Therefore, we can conclude that the correct equation equivalent to the given expression in the question can be seen in Option b.
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