Question

1. andre solved an equation, but when he checked his answer he saw his solution was incorrect. he knows he made a mistake, but he cant find it. where is andres mistake and what is the solution to the equation? -2(3x - 5) = 4(x + 3) + 8 -6x + 10 = 4x + 12 + 8 -6x + 10 = 4x + 20 10 = -2x + 20 -10 = -2x 5 = x

Explanation:

Step1: Locate Andre's error

When moving $-6x$ to the right and $4x$ to the left, Andre incorrectly calculated the coefficient of $x$. The correct step should be isolating the $x$-terms:
Starting from $-6x + 10 = 4x + 20$, subtract $4x$ from both sides and subtract 10 from both sides:
$-6x - 4x = 20 - 10$

Step2: Simplify both sides

Calculate the left and right hand sides:
$-10x = 10$

Step3: Solve for $x$

Divide both sides by $-10$:
$x = \frac{10}{-10}$

Answer:

Andre made a mistake when rearranging the $x$-terms: he incorrectly calculated $-6x - 4x$ as $-2x$ instead of $-10x$. The correct solution is $x = -1$.