How many solutions does the equation -4(x+5)=-4x-20 have?

sublimnoj7u7

sublimnoj7u7

Answered question

2023-01-06

How many solutions does the equation 4(x+5)=4x20 have?

Answer & Explanation

Mikayla Cox

Mikayla Cox

Beginner2023-01-07Added 15 answers

Increasing the bracket results in:
4x20=4x20
4x+4x=2020
0=0 Which is true
After speaking with a friend, I've been told that the following is applicable:
The outcome is always zero on both sides and thus always true. From this it means that despite this one outcome you can allocated any value to x. So there is a infinite number of solutions.
Kadyn Acevedo

Kadyn Acevedo

Beginner2023-01-08Added 1 answers

One way to approach this is to start with an equation that can be seen to satisfy any value of x, and then use that equation to derive the given equation.
Begin with it:
x=x
Add 5 to both sides to get:
x+5=x+5
Multiply both sides by -4 to get:
4(x+5)=4(x+5)
Expand the right hand side using distributivity to get:
4(x+5)=4x20
So this holds for any value of x
So there are infinitely many solutions (in fact uncountably infinitely many solutions).

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