Question

paloma used these steps to solve the equation $6x + 5 = 3(2x + 1)$. which choice describes the meaning of her result, $2 = 0$?
step 1: $6x + 5 = 3(2x + 1)$
step 2: $6x + 5 = 6x + 3$
step 3: $- 3$
$6x + 5 - 3 = 6x + 3 - 3$
step 4: $6x + 2 = 6x$
step 5: $-6x$
$6x + 2 - 6x = 6x - 6x$
step 6: $2 = 0$
options:
the solution is $x = 2$.
all values of $x$ make the equation true.
the result is not correct because step 2 has an error.
no values of $x$ make the equation true.

Explanation:

Step1: Expand the right - hand side of the equation

Expand \(3(2x + 1)\) using the distributive property \(a(b + c)=ab+ac\). Here \(a = 3\), \(b=2x\), \(c = 1\), so \(3(2x + 1)=6x+3\). The original equation \(6x + 5=3(2x + 1)\) becomes \(6x + 5=6x+3\).

Step2: Subtract \(6x\) from both sides

Subtract \(6x\) from the left - hand side \(6x + 5-6x=5\) and from the right - hand side \(6x+3 - 6x=3\). We get \(5 = 3\).

Since \(5
eq3\) is a contradiction, there is no value of \(x\) that makes the equation \(6x + 5=3(2x + 1)\) true.

Answer:

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