Solve for x and write your answer in simplest form. -6x+6(-2x+(3)/(2))-6=-(5)/(2)(2x-2) Answer: x=

Distribute and Simplify: First, let's distribute the 6 into the parentheses on the left side of the equation and the -5/2 into the parentheses on the right side of the equation. -6x + 6(-2x + 3/2) - 6 = -(5/2)(2x - 2) -6x - 12x + 9 - 6 = -5x + 5Combine Like Terms: Now, let's combine like terms on both sides of the equation. (-6x - 12x) + (9 - 6) = -5x + 5 -18x + 3 = -5x + 5Move Terms and Constants: Next, we will move all terms containing x to one side of the equation and the constant terms to the other side. -18x + 5x = 5 - 3 -13x = 2Solve for x: Now, we will divide both sides of the equation by -13 to solve for x. x = 2 / -13 x = -2 / 13

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Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. Solve for

x

and write your answer in simplest form.

\newline

-6 x+6\left(-2 x+\frac{3}{2}\right)-6=-\frac{5}{2}(2 x-2)

\newline

Answer:

x=

Distribute and Simplify: First, let's distribute the $6$ into the parentheses on the left side of the equation and the $-\frac{5}{2}$ into the parentheses on the right side of the equation. $\newline$ $-6x + 6(-2x + \frac{3}{2}) - 6 = -\left(\frac{5}{2}\right)(2x - 2)$ $\newline$ $-6x - 12x + 9 - 6 = -5x + 5$
Combine Like Terms: Now, let's combine like terms on both sides of the equation. $\newline$ $(-6x - 12x) + (9 - 6) = -5x + 5$ $\newline$ $-18x + 3 = -5x + 5$
Move Terms and Constants: Next, we will move all terms containing $x$ to one side of the equation and the constant terms to the other side. $-18x + 5x = 5 - 3$ $-13x = 2$
Solve for x: Now, we will divide both sides of the equation by $-13$ to solve for x. $\newline$ $x = \frac{2}{-13}$ $\newline$ $x = \frac{-2}{13}$