Solve using the multiplication and addition principles together.​ Don't forget to check.

99xminus−11equals=44

To solve the equation \(99x - 11 = 44\) using the multiplication and addition principles, follow these steps:

### Step 1: Add 11 to both sides of the equation.
This step aims to isolate the term with \(x\) on one side.

\[
99x - 11 + 11 = 44 + 11
\]

Simplifying both sides:

\[
99x = 55
\]

### Step 2: Divide both sides by 99 to solve for \(x\).

\[
x = \frac{55}{99}
\]

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 11:

\[
x = \frac{55 \div 11}{99 \div 11} = \frac{5}{9}
\]

### Step 3: Check the solution.
Substitute \(x = \frac{5}{9}\) back into the original equation to verify.

Original equation:

\[
99x - 11 = 44
\]

Substitute \(x = \frac{5}{9}\):

\[
99 \times \frac{5}{9} - 11 = 44
\]

Simplify \(99 \times \frac{5}{9}\):

\[
\frac{99 \times 5}{9} = \frac{495}{9} = 55
\]

So,

\[
55 - 11 = 44
\]

Since both sides of the equation are equal, the solution \(x = \frac{5}{9}\) is correct.

Would you like any further details or have any questions?

Here are some related questions:
1. How do you determine the greatest common divisor (GCD) of two numbers?
2. Can you explain the steps involved in simplifying a fraction?
3. What is the purpose of checking a solution in an equation?
4. How can the multiplication principle be applied in more complex equations?
5. How does the addition principle work in solving equations with variables?

**Tip:** When solving equations, always perform the same operation on both sides to maintain balance.

Learn how to solve equations using the multiplication and addition principles. This problem involves solving the equation 99x - 11 = 44 step-by-step, covering key algebraic concepts such as equations, fractions, and basic arithmetic operations. Suitable for students in Grades 7-9.

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