UGA Math Placement Practice Exam

What is the solution to the equation 2x + 3 = 11?

x = 4 x = 5 x = 6 x = 7

Correct Answer:

x = 4

Explanation:

To solve the equation \(2x + 3 = 11\), the goal is to isolate the variable \(x\). Start by eliminating the constant term on the left side. This can be achieved by subtracting 3 from both sides of the equation: \[ 2x + 3 - 3 = 11 - 3 \] This simplifies to: \[ 2x = 8 \] Next, to isolate \(x\), divide both sides by 2: \[ \frac{2x}{2} = \frac{8}{2} \] This simplifies to: \[ x = 4 \] Thus, the solution to the equation is \(x = 4\). This value satisfies the original equation, confirming its correctness. When substituted back into the equation, it yields \(2(4) + 3 = 8 + 3 = 11\), which holds true.

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