Question

(2x-1)(6x+2)>(3x-1)(4x+1)

Answer 1

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Answer 2

To solve the inequality $(2x-1)(6x+2) > (3x-1)(4x+1)$, we'll follow these steps:

1. Expand both sides of the inequality.
2. Simplify the expressions.
3. Solve for $x$ by isolating it on one side of the inequality.

Let's go through these steps:

Step 1: Expand both sides of the inequality:

$$12x^2 + 4x - 6x - 2 > 12x^2 + 4x - 3x - x - 1$$

Step 2: Simplify the expressions:

$$12x^2 + 4x - 6x - 2 > 12x^2 + x - 1$$

Step 3: Simplify further and solve for $x$:

$$12x^2 - 2 > 12x^2 + x - 1$$

Subtract $12x^2$ from both sides:

$$-2 > x - 1$$

Now, add $1$ to both sides:

$$-1 > x$$

So, the solution to the inequality is $x < -1$.