Isolate the variable x: Isolate the variable x by multiplying both sides of the equation by the reciprocal of the coefficient of x. The reciprocal of 2/7 is 7/2. So, we multiply both sides of the equation by 7/2 to isolate x. (7/2) * (2/7)x = (7/2) * -14Simplify both sides: Simplify both sides of the equation. On the left side, (7/2) * (2/7) simplifies to 1, leaving us with x. On the right side, (7/2) * -14 simplifies to -49. So, x = -49.Check the solution: Check the solution by substituting the value of x back into the original equation. (2/7)(-49) should equal -14. (2/7)(-49) = -98/7 = -14, which is true.

Grade 8

Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for x.

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(\frac{2}{7})x= -14

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x =

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Isolate the variable x: Isolate the variable x by multiplying both sides of the equation by the reciprocal of the coefficient of x. $\newline$ The reciprocal of $\frac{2}{7}$ is $\frac{7}{2}$ . So, we multiply both sides of the equation by $\frac{7}{2}$ to isolate x. $\newline$ $\left(\frac{7}{2}\right) \cdot \left(\frac{2}{7}\right)x = \left(\frac{7}{2}\right) \cdot -14$
Simplify both sides: Simplify both sides of the equation. $\newline$ On the left side, $(\frac{7}{2}) \times (\frac{2}{7})$ simplifies to $1$ , leaving us with $x$ . $\newline$ On the right side, $(\frac{7}{2}) \times -14$ simplifies to $-49$ . $\newline$ So, $x = -49$ .
Check the solution: Check the solution by substituting the value of $x$ back into the original equation. $\newline$ $(\frac{2}{7})(-49)$ should equal $-14$ . $\newline$ $(\frac{2}{7})(-49) = \frac{-98}{7} = -14$ , which is true.