Which value of x satisfies the equation (3)/(4)(x-(1)/(5))=-(69)/(10) ? 9 10 -10 -9

Write Equation: Write down the equation to be solved. (3/4)(x - 1/5) = -69/10Multiply by Reciprocal: Multiply both sides of the equation by the reciprocal of (3/4) to isolate the term with x. Reciprocal of (3/4) is (4/3). (4/3) * (3/4)(x - 1/5) = (4/3) * (-69/10)Simplify Equation: Simplify both sides of the equation. The left side simplifies to x - 1/5 because (4/3) * (3/4) = 1. The right side simplifies to -69/10 * 4/3. x - 1/5 = -69/10 * 4/3Calculate Right Side: Calculate the right side of the equation. -69/10 * 4/3 = -276/30 Simplify -276/30 by dividing both numerator and denominator by 6. -276/30 = -46/5 x - 1/5 = -46/5Add 1/5: Add 1/5 to both sides of the equation to solve for x. x - 1/5 + 1/5 = -46/5 + 1/5 x = -46/5 + 1/5Combine Fractions: Combine the fractions on the right side of the equation. -46/5 + 1/5 = (-46 + 1)/5 -45/5 = -9 x = -9

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Which value of
x satisfies the equation
(3)/(4)(x-(1)/(5))=-(69)/(10) ?
9
10

-10

-9

Which value of $x$ satisfies the equation $\frac{3}{4}\left(x-\frac{1}{5}\right)=-\frac{69}{10}$ ? $\newline$ $9$ $\newline$ $10$ $\newline$ $-10$ $\newline$ $-9$

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Math Problems

Algebra 1

Evaluate integers raised to rational exponents

Full solution

Q. Which value of

x

satisfies the equation

\frac{3}{4}\left(x-\frac{1}{5}\right)=-\frac{69}{10}

\newline

9

\newline

10

\newline

-10

\newline

-9

Write Equation: Write down the equation to be solved. $\newline$ $(\frac{3}{4})(x - \frac{1}{5}) = -\frac{69}{10}$
Multiply by Reciprocal: Multiply both sides of the equation by the reciprocal of $(\frac{3}{4})$ to isolate the term with $x$ . $\newline$ Reciprocal of $(\frac{3}{4})$ is $(\frac{4}{3})$ . $\newline$ $(\frac{4}{3}) \times (\frac{3}{4})(x - \frac{1}{5}) = (\frac{4}{3}) \times (\frac{-69}{10})$
Simplify Equation: Simplify both sides of the equation. $\newline$ The left side simplifies to $x - \frac{1}{5}$ because $(\frac{4}{3}) \times (\frac{3}{4}) = 1$ . $\newline$ The right side simplifies to $-\frac{69}{10} \times \frac{4}{3}$ . $\newline$ $x - \frac{1}{5} = -\frac{69}{10} \times \frac{4}{3}$
Calculate Right Side: Calculate the right side of the equation. $\newline$ $-\frac{69}{10} \times \frac{4}{3} = -\frac{276}{30}$ $\newline$ Simplify $-\frac{276}{30}$ by dividing both numerator and denominator by $6$ . $\newline$ $-\frac{276}{30} = -\frac{46}{5}$ $\newline$ $x - \frac{1}{5} = -\frac{46}{5}$
Add $\frac{1}{5}$ : Add $\frac{1}{5}$ to both sides of the equation to solve for $x$ . $x - \frac{1}{5} + \frac{1}{5} = -\frac{46}{5} + \frac{1}{5}$ $x = -\frac{46}{5} + \frac{1}{5}$
Combine Fractions: Combine the fractions on the right side of the equation. $\newline$ $-\frac{46}{5} + \frac{1}{5} = \frac{-46 + 1}{5}$ $\newline$ $-\frac{45}{5} = -9$ $\newline$ $x = -9$