Question

solve the following equation by using the addition principle. check the solution.
$-\frac{5}{6} + y = -\frac{3}{4}$

the solution is $y = \square$. (type an integer or a simplified fraction.)

Explanation:

Step1: Isolate y via addition principle

Add $\frac{5}{6}$ to both sides:
$$-\frac{5}{6} + y + \frac{5}{6} = -\frac{3}{4} + \frac{5}{6}$$

Step2: Simplify left side

Left side simplifies to $y$:
$$y = -\frac{3}{4} + \frac{5}{6}$$

Step3: Find common denominator (12)

Rewrite fractions with denominator 12:
$$y = -\frac{9}{12} + \frac{10}{12}$$

Step4: Add the fractions

Combine the numerators:
$$y = \frac{-9 + 10}{12} = \frac{1}{12}$$

Step5: Verify solution

Substitute $y=\frac{1}{12}$ into original equation:
$$-\frac{5}{6} + \frac{1}{12} = -\frac{10}{12} + \frac{1}{12} = -\frac{9}{12} = -\frac{3}{4}$$
This matches the right-hand side, so the solution is valid.

Answer:

$\frac{1}{12}$