Question

In Exercises \(32-37\), solve each equation for the unknown quantity. Check your answers. $$x-\frac{2}{3}=\frac{1}{15}$$

Short answer

Answer: The value of x is \(\frac{11}{15}\).

Step-by-step solution

Eliminate the fraction.

To eliminate the fraction, we want to multiply the entire equation by the lowest common multiple of the denominators, which is 15. This will give us a linear equation without fractions: $$(15)(x-\frac{2}{3}=\frac{1}{15})$$ $$15x-10=1$$

Move the constant to the right side.

Now, we want to isolate x by adding the constant 10 to both sides of the equation: $$15x-10+10=1+10$$ $$15x=11$$

Solve for x.

To solve for x, divide both sides by 15: $$x=\frac{11}{15}$$

Check the solution.

To make sure the solution is correct, plug the value of x back into the original equation to see if it is true: $$\frac{11}{15}-\frac{2}{3}=\frac{1}{15}$$ $$\frac{11}{15}-\frac{10}{15}=\frac{1}{15}$$ $$\frac{1}{15}=\frac{1}{15}$$ Since the solution checks out, x = \(\frac{11}{15}\) is the correct answer.