Question

(x+3)(x-4)-(x-7)(x-2)=-2

Answer 1

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Answer 2

To solve the equation $(x+3)(x-4)-(x-7)(x-2)=-2$, you can start by expanding both sets of parentheses and then simplifying the equation:

$(x+3)(x-4) - (x-7)(x-2) = -2$

Expanding the first set of parentheses:

$x^2 - 4x + 3x - 12$

Expanding the second set of parentheses:

$x^2 - 2x - 7x + 14$

Now, let's simplify the equation:

$(x^2 - 4x + 3x - 12) - (x^2 - 2x - 7x + 14) = -2$

Combine like terms within each set of parentheses:

$(x^2 - x - 12) - (x^2 - 9x + 14) = -2$

Now, distribute the negative sign to the terms within the second set of parentheses:

$x^2 - x - 12 - x^2 + 9x - 14 = -2$

Now, combine like terms on both sides of the equation:

$-x - 12 - 9x - 14 = -2$

Combine the constants on the left side:

$-10x - 26 = -2$

Next, add 26 to both sides of the equation to isolate the term with x:

$-10x = 24$

Finally, divide both sides by -10 to solve for x:

$x = \frac{24}{-10} = -\frac{12}{5}$

So, the solution to the equation is:

$x = -\frac{12}{5}$