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Which value of
x satisfies the equation
(3)/(5)(x-(1)/(4))=-(15)/(4) ?

-7

-6
7
6

Which value of $x$ satisfies the equation $\frac{3}{5}\left(x-\frac{1}{4}\right)=-\frac{15}{4}$ ? $\newline$ $-7$ $\newline$ $-6$ $\newline$ $7$ $\newline$ $6$

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Add and subtract three or more integers

Full solution

Q. Which value of

x

satisfies the equation

\frac{3}{5}\left(x-\frac{1}{4}\right)=-\frac{15}{4}

?

\newline

-7

\newline

-6

\newline

7

\newline

6

Write Equation: Write down the equation that needs to be solved. $\newline$ $(\frac{3}{5})(x - \frac{1}{4}) = -\frac{15}{4}$
Eliminate Fraction: To isolate $x$ , we first need to get rid of the fraction on the left side by multiplying both sides of the equation by the reciprocal of $\frac{3}{5}$ , which is $\frac{5}{3}$ .
Multiply both sides by $\frac{5}{3}$ :
\left(\frac{\(5\)}{\(3\)}\right) \times \left(\frac{\(3\)}{\(5\)}\right)(x - \frac{\(1\)}{\(4\)}) = \left(\frac{\(5\)}{\(3\)}\right) \times \left(-\frac{\(15\)}{\(4\)}\right)
Simplify Equation: Simplify both sides of the equation. On the left side, the \(\frac{5}{3} and $\frac{3}{5}$ cancel each other out, leaving us with $x - \frac{1}{4}$ . On the right side, we multiply the numerators and denominators. $\newline$ $x - \frac{1}{4} = \frac{(5 \times -15)}{(3 \times 4)}$ $\newline$ $x - \frac{1}{4} = \frac{-75}{12}$
Isolate $x$ : Simplify the fraction on the right side by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $\newline$ $x - \frac{1}{4} = \frac{-75 / 3}{12 / 3}$ $\newline$ $x - \frac{1}{4} = -\frac{25}{4}$
Combine Fractions: Now, we need to isolate $x$ by adding $\frac{1}{4}$ to both sides of the equation. $\newline$ $x = -\frac{25}{4} + \frac{1}{4}$
Simplify $x$ : Combine the fractions on the right side by finding a common denominator, which is already $4$ , and then adding the numerators. $\newline$ $x = (-25 + 1) / 4$ $\newline$ $x = -24 / 4$
Simplify $x$ : Combine the fractions on the right side by finding a common denominator, which is already $4$ , and then adding the numerators. $\newline$ $x = (-25 + 1) / 4$ $\newline$ $x = -24 / 4$ Simplify the fraction on the right side by dividing the numerator by the denominator. $\newline$ $x = -24 / 4$ $\newline$ $x = -6$

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