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How many solutions are there to the equation below?

4x + 47 = 4(x + 5)

A. No solution
B. Infinitely many solutions
C. One solution

Sagot :

GinnyAnsweridn
To determine the number of solutions to the equation [tex]\( 4x + 47 = 4(x + 5) \)[/tex], let's work through it step by step.

1. Start with the given equation:
[tex]\[ 4x + 47 = 4(x + 5) \][/tex]

2. Distribute the 4 on the right-hand side:
[tex]\[ 4x + 47 = 4x + 20 \][/tex]

3. Subtract [tex]\( 4x \)[/tex] from both sides to simplify:
[tex]\[ 47 = 20 \][/tex]

4. Analyze the resulting statement:
[tex]\[ 47 = 20 \][/tex]
This statement is clearly false since 47 is not equal to 20.

Since this contradiction arises, it means that there are no values of [tex]\( x \)[/tex] that can satisfy the original equation. Therefore, the equation has:

A. No solution

So, the correct answer is:
A. No solution
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