Question

\(3 - 2x^2 - [-x(1+2x)] = -5\)
Column A: x
Column B: -8

• A. Quantity A is greater
• B. Quantity B is greater
• C. The two quantities are equal
• D. The relationship cannot be determined from the information given

Hint:

Always simplify complex algebraic equations before assuming they are difficult to solve. Look for terms that might cancel out, as often happens in these types of problems.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question requires solving a linear equation for the variable \(x\). The presence of \(x^2\) terms might suggest a quadratic equation, but we should simplify first to see if they cancel out.
Step 2: Detailed Explanation:
Let's simplify the given equation step-by-step.
\[ 3 - 2x^2 - [-x(1+2x)] = -5 \] First, distribute the \(-x\) inside the brackets:
\[ 3 - 2x^2 - [-x - 2x^2] = -5 \] Next, distribute the negative sign in front of the brackets:
\[ 3 - 2x^2 + x + 2x^2 = -5 \] The \(-2x^2\) and \(+2x^2\) terms cancel each other out.
\[ 3 + x = -5 \] Now, solve for \(x\) by subtracting 3 from both sides:
\[ x = -5 - 3 \] \[ x = -8 \] Step 3: Comparing the Quantities:
Column A: \(x\), which we found to be -8.
Column B: -8.
The two quantities are equal.