What is the solution to the equation 2(x - 3) = 4?

What is the solution to the equation 2(x - 3) = 4?

• A. 3
• B. 6
• C. 7
• D. 4

Answer: (C)

To solve the equation \(2(x - 3) = 4\), we start by distributing the 2 on the left side of the equation: \[ 2 \cdot x - 2 \cdot 3 = 4 \] which simplifies to: \[ 2x - 6 = 4 \] Next, we isolate the term with \(x\) by adding 6 to both sides of the equation: \[ 2x - 6 + 6 = 4 + 6 \] This simplifies to: \[ 2x = 10 \] Now, we solve for \(x\) by dividing both sides by 2: \[ x = \frac{10}{2} = 5 \] Thus, the correct solution to the equation is \(5\). In assessing the provided answer of 7, it is important to note that it does not satisfy the original equation upon substitution. This illustrates the need to carefully carry out algebraic steps to find the accurate solution. The answer reflects a misunderstanding of the operations necessary to isolate the variable in the equation.

To solve the equation (2(x - 3) = 4), we start by distributing the 2 on the left side of the equation:

[

2 \cdot x - 2 \cdot 3 = 4

]

which simplifies to:

[

2x - 6 = 4

]

Next, we isolate the term with (x) by adding 6 to both sides of the equation:

[

2x - 6 + 6 = 4 + 6

]

This simplifies to:

[

2x = 10

]

Now, we solve for (x) by dividing both sides by 2:

[

x = \frac{10}{2} = 5

]

Thus, the correct solution to the equation is (5).

In assessing the provided answer of 7, it is important to note that it does not satisfy the original equation upon substitution. This illustrates the need to carefully carry out algebraic steps to find the accurate solution. The answer reflects a misunderstanding of the operations necessary to isolate the variable in the equation.