Solve for x and write your answer in simplest form. -5(x-4)-7x=5((2)/(5)x+(8)/(5))-9 Answer: x=

Distribute and Simplify: First, distribute the -5 into the parentheses on the left side of the equation and the 5 into the parentheses on the right side of the equation. -5(x - 4) - 7x = 5((2/5)x + (8/5)) - 9 -5x + 20 - 7x = 2x + 8 - 9Combine Like Terms: Combine like terms on both sides of the equation. (-5x - 7x) + 20 = (2x) + (8 - 9) -12x + 20 = 2x - 1Isolate x Terms: Next, move all terms involving x to one side of the equation and the constant terms to the other side. -12x - 2x = -1 - 20 -14x = -21Solve for x: Divide both sides of the equation by -14 to solve for x. x = (-21) / (-14) x = 21/14Final Simplification: Simplify the fraction 21/14 by dividing both the numerator and the denominator by their greatest common divisor, which is 7. x = (21/7) / (14/7) x = 3 / 2

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Precalculus

Find the roots of factored polynomials

Full solution

Q. Solve for

x

and write your answer in simplest form.

\newline

-5(x-4)-7 x=5\left(\frac{2}{5} x+\frac{8}{5}\right)-9

\newline

Answer:

x=

Distribute and Simplify: First, distribute the $-5$ into the parentheses on the left side of the equation and the $5$ into the parentheses on the right side of the equation. $-5(x - 4) - 7x = 5\left(\frac{2}{5}x + \frac{8}{5}\right) - 9$ $-5x + 20 - 7x = 2x + 8 - 9$
Combine Like Terms: Combine like terms on both sides of the equation. $\newline$ $(-5x - 7x) + 20 = (2x) + (8 - 9)$ $\newline$ $-12x + 20 = 2x - 1$
Isolate x Terms: Next, move all terms involving $x$ to one side of the equation and the constant terms to the other side. $-12x - 2x = -1 - 20$ $-14x = -21$
Solve for x: Divide both sides of the equation by $-14$ to solve for x. $\newline$ $x = \frac{-21}{-14}$ $\newline$ $x = \frac{21}{14}$
Final Simplification: Simplify the fraction $\frac{21}{14}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $7$ .
$x = \frac{(21/7)}{(14/7)}$
$x = \frac{3}{2}$