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(x - 2)(x + 4)-(x - 3)(x - 1) = 0...

`(x - 2)(x + 4)-(x - 3)(x - 1) = 0`

A

`-5`

B

`-1`

C

`0`

D

`11//6`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \((x - 2)(x + 4) - (x - 3)(x - 1) = 0\), we will follow these steps: ### Step 1: Expand both products First, we will expand the two products in the equation. \[ (x - 2)(x + 4) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8 \] \[ (x - 3)(x - 1) = x^2 - x - 3x + 3 = x^2 - 4x + 3 \] ### Step 2: Substitute the expanded forms back into the equation Now we substitute the expanded forms back into the original equation: \[ (x^2 + 2x - 8) - (x^2 - 4x + 3) = 0 \] ### Step 3: Simplify the equation Next, we simplify the equation by distributing the negative sign and combining like terms: \[ x^2 + 2x - 8 - x^2 + 4x - 3 = 0 \] This simplifies to: \[ (2x + 4x) + (-8 - 3) = 0 \] \[ 6x - 11 = 0 \] ### Step 4: Solve for \(x\) Now, we will solve for \(x\): \[ 6x = 11 \] \[ x = \frac{11}{6} \] ### Final Answer Thus, the solution to the equation \((x - 2)(x + 4) - (x - 3)(x - 1) = 0\) is: \[ x = \frac{11}{6} \]
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