c. $$ \frac{9}{10}-\frac{4}{5} m=\frac{5}{6} $$ $$ m=\square $$ (Simplify your answer. Type an integer, fraction, or mixed number

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{9}{10} - \frac{4}{5}m = \frac{5}{6}
$$

**Step 1:** Subtract $$\frac{9}{10}$$ from both sides to isolate the term with $$m$$:

$$
-\frac{4}{5}m = \frac{5}{6} - \frac{9}{10}
$$

**Step 2:** Find a common denominator to subtract the fractions on the right side. The least common denominator (LCD) of 6 and 10 is 30.

$$
\frac{5}{6} = \frac{25}{30} \quad \text{and} \quad \frac{9}{10} = \frac{27}{30}
$$

So,

$$
\frac{5}{6} - \frac{9}{10} = \frac{25}{30} - \frac{27}{30} = -\frac{2}{30} = -\frac{1}{15}
$$

Now the equation is:

$$
-\frac{4}{5}m = -\frac{1}{15}
$$

**Step 3:** Multiply both sides by $$-1$$ to make the coefficient of $$m$$ positive:

$$
\frac{4}{5}m = \frac{1}{15}
$$

**Step 4:** Solve for $$m$$ by multiplying both sides by the reciprocal of $$\frac{4}{5}$$, which is $$\frac{5}{4}$$:

$$
m = \frac{1}{15} \times \frac{5}{4} = \frac{5}{60} = \frac{1}{12}
$$

**Final Answer:**

$$
m = \frac{1}{12}
$$
$$ m = \frac{1}{12} $$

c. \( \frac{9}{10}-\frac{4}{5} m=\frac{5}{6} \) \( m=\square \) (Simplify your answer. Type an integer, fraction, or mixed number