Solve for a,a.
minus, 21, plus, start fraction, 11, divided by, 12, end fraction, a, equals, 45
−21+ 
12
11
​
 a=
45

We are given the equation:

\[
-21 + \frac{11}{12}a = 45
\]

Let's solve for \( a \) step by step.

### Step 1: Isolate the term with \( a \)
Add 21 to both sides to eliminate the constant term on the left side:

\[
-21 + \frac{11}{12}a + 21 = 45 + 21
\]

This simplifies to:

\[
\frac{11}{12}a = 66
\]

### Step 2: Solve for \( a \)
To get \( a \) by itself, multiply both sides of the equation by the reciprocal of \( \frac{11}{12} \), which is \( \frac{12}{11} \):

\[
a = 66 \times \frac{12}{11}
\]

Simplify the right-hand side:

\[
a = \frac{66 \times 12}{11} = \frac{792}{11} = 72
\]

### Final Answer:
\[
a = 72
\]

Would you like more details on any step, or have any questions?

Here are 5 related questions:
1. What happens if you change the constant 45 to another value?
2. Can you solve a similar equation with a different fraction coefficient?
3. How do you check if the solution \( a = 72 \) is correct?
4. What would change if the equation had a subtraction instead of addition of the fraction term?
5. How do you solve an equation when the fraction includes variables in both the numerator and denominator?

**Tip:** When solving equations with fractions, multiplying by the reciprocal of the fraction can help eliminate it easily.

Explore how to solve a linear equation with a fractional coefficient: -21 + (11/12)a = 45. This detailed step-by-step guide covers algebraic concepts like isolating variables and working with fractions. Ideal for Grades 6-8 students learning linear equations.

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