Question

analyzing solution sets to linear equations with the variable on both sides - item 3457
paloma used these steps to solve the equation ( 6 x + 5 = 3 ( 2 x + 1 ) ). which choice
describes the meaning of her result, ( 2 = 0 )?
step 1 ( 6 x + 5 = 3 ( 2 x + 1 ) )
step 2 ( 6 x + 5 = 6 x + 3 )
step 3 ( \frac { - 3 quad - 3 } { 6 x + 2 = 6 x } )
step 4 ( 6 x + 2 = 6 x )
step 5 ( \frac { - 6 x quad - 6 x } { 2 = 0 } )
step 6
the solution is ( x = 2 ).
the result is not correct because step 2 has an error.
all values of ( x ) make the equation true.
no values of ( x ) make the equation true.

Explanation:

Step1: Analyze the equation

An equation \(a = b\) where \(a
eq b\) (here \(2 = 0\)) implies no solution.

Step2: Interpret the result

When solving an equation, if we end up with a false statement (a contradiction) like \(2 = 0\), it means there are no values of the variable (\(x\) in this case) that can satisfy the original equation.

Answer:

No values of \(x\) make the equation true.