Which value of $x$ satisfies the equation $\frac{2}{3}\left(x-\frac{1}{4}\right)=\frac{19}{6}$ ? $\newline$ $6$ $\newline$ $5$ $\newline$ $-5$ $\newline$ $-6$

Full solution

Q. Which value of

x

satisfies the equation

\frac{2}{3}\left(x-\frac{1}{4}\right)=\frac{19}{6}

\newline

6

\newline

5

\newline

-5

\newline

-6

Write Equation: Write down the equation to be solved. $\newline$ $(\frac{2}{3})(x - \frac{1}{4}) = \frac{19}{6}$
Multiply by Reciprocal: Multiply both sides of the equation by the reciprocal of $(\frac{2}{3})$ to isolate the term with $x$ . The reciprocal of $(\frac{2}{3})$ is $(\frac{3}{2})$ . Multiplying both sides by $(\frac{3}{2})$ gives: $(\frac{3}{2}) \times (\frac{2}{3})(x - \frac{1}{4}) = (\frac{3}{2}) \times (\frac{19}{6})$
Simplify Equation: Simplify both sides of the equation. $\newline$ On the left side, $(\frac{3}{2}) \times (\frac{2}{3}) = 1$ , so we are left with $x - \frac{1}{4}$ . $\newline$ On the right side, $(\frac{3}{2}) \times (\frac{19}{6}) = (\frac{3 \times 19}{2 \times 6}) = \frac{57}{12} = \frac{19}{4}$ . $\newline$ So, the equation simplifies to: $\newline$ $x - \frac{1}{4} = \frac{19}{4}$
Add $\frac{1}{4}$ : Add $\frac{1}{4}$ to both sides of the equation to solve for $x$ . $x - \frac{1}{4} + \frac{1}{4} = \frac{19}{4} + \frac{1}{4}$ $x = \frac{19}{4} + \frac{1}{4}$
Combine Fractions: Combine the fractions on the right side of the equation. $\newline$ $\frac{19}{4} + \frac{1}{4} = \frac{19 + 1}{4} = \frac{20}{4}$ $\newline$ $x = \frac{20}{4}$
Simplify Fraction: Simplify the fraction on the right side of the equation to find the value of $x$ . $\frac{20}{4} = 5$ $x = 5$