Solve the following equation for x. Express your answer in the simplest form.
2 (-4x-6)=-2(4x+6)
To solve the equation 2(-4x-6) = -2(4x+6) for x, we will follow these steps:
Step 1: Distribute the coefficients to the terms inside the parentheses on both sides of the equation.
2 * -4x + 2 * (-6) = -2 * 4x + -2 * 6
This simplifies the equation to:
-8x - 12 = -8x - 12
Step 2: Combine like terms. Notice that both sides of the equation have the same terms, so we can observe that they are equal, resulting in an identity equation.
Since both sides are identical, there are infinitely many solutions for x. No matter what value you choose for x, the equation will still be true.
Therefore, the solution is all real numbers for x. In interval notation, we can answer this as (-∞, +∞).