Which value of x satisfies the equation (5)/(4)(x-(2)/(3))=(125)/(12) ? 8 -9 -8 9

Identify equation: Identify the equation to solve. We have the equation (5/4)(x - 2/3) = 125/12. Our goal is to find the value of x that satisfies this equation.Clear fractions: Clear the fraction on the left side by multiplying both sides of the equation by the reciprocal of 5/4, which is 4/5. (4/5) * (5/4)(x - 2/3) = (4/5) * (125/12)Simplify left side: Simplify the left side of the equation. (4/5) * (5/4) simplifies to 1, so we are left with x - 2/3 on the left side. x - 2/3 = (4/5) * (125/12)Perform multiplication: Perform the multiplication on the right side of the equation. (4/5) * (125/12) = (4 * 125) / (5 * 12) = 500 / 60 = 50 / 6 = 25 / 3 So, x - 2/3 = 25/3Add 2/3: Add 2/3 to both sides of the equation to isolate x. x - 2/3 + 2/3 = 25/3 + 2/3 x = 25/3 + 2/3Add fractions: Add the fractions on the right side of the equation. 25/3 + 2/3 = (25 + 2) / 3 = 27 / 3 x = 27 / 3Simplify fraction: Simplify the fraction on the right side to find the value of x. 27 / 3 = 9 So, x = 9

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which value of
x satisfies the equation
(5)/(4)(x-(2)/(3))=(125)/(12) ?
8

-9

-8
9

Which value of $x$ satisfies the equation $\frac{5}{4}\left(x-\frac{2}{3}\right)=\frac{125}{12}$ ? $\newline$ $8$ $\newline$ $-9$ $\newline$ $-8$ $\newline$ $9$

View step-by-step help

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Which value of

x

satisfies the equation

\frac{5}{4}\left(x-\frac{2}{3}\right)=\frac{125}{12}

\newline

8

\newline

-9

\newline

-8

\newline

9

Identify equation: Identify the equation to solve. $\newline$ We have the equation $(\frac{5}{4})(x - \frac{2}{3}) = \frac{125}{12}$ . Our goal is to find the value of $x$ that satisfies this equation.
Clear fractions: Clear the fraction on the left side by multiplying both sides of the equation by the reciprocal of $\frac{5}{4}$ , which is $\frac{4}{5}$ .\left(\frac{$4$}{$5$}\right) \times \left(\frac{$5$}{$4$}\right)(x - \frac{$2$}{$3$}) = \left(\frac{$4$}{$5$}\right) \times \left(\frac{$125$}{$12$}\right)
Simplify left side: Simplify the left side of the equation.\(\newline $(\frac{4}{5}) \times (\frac{5}{4})$ simplifies to $1$ , so we are left with $x - \frac{2}{3}$ on the left side. $\newline$ $x - \frac{2}{3} = (\frac{4}{5}) \times (\frac{125}{12})$
Perform multiplication: Perform the multiplication on the right side of the equation. $\newline$ (\frac{$4$}{$5$}) \times (\frac{$125$}{$12$}) = (\frac{$4$ \times $125$}{$5$ \times $12$})\(\newline= \frac{ $500$ }{ $60$ } $\newline$ = \frac{ $50$ }{ $6$ } $\newline$ = \frac{ $25$ }{ $3$ } $\newline$ So, x - \frac{ $2$ }{ $3$ } = \frac{ $25$ }{ $3$ }
Add $\frac{2}{3}$ : Add $\frac{2}{3}$ to both sides of the equation to isolate $x$ .
$x - \frac{2}{3} + \frac{2}{3} = \frac{25}{3} + \frac{2}{3}$
$x = \frac{25}{3} + \frac{2}{3}$
Add fractions: Add the fractions on the right side of the equation. $\newline$ $\frac{25}{3} + \frac{2}{3} = \frac{(25 + 2)}{3}$ $\newline$ $= \frac{27}{3}$ $\newline$ $x = \frac{27}{3}$
Simplify fraction: Simplify the fraction on the right side to find the value of $x$ . $\frac{27}{3} = 9$ So, $x = 9$