In Exercises 99–106, solve each equation. [(3 + 6)^2 ÷ 3] × 4 = - 54 x

Verified step by step guidance

1. First, simplify the expression inside the parentheses: $3+6$.
2. Next, square the result from the first step: $(3+6{)}^2$.
3. Then, divide the squared result by 3: $\frac{(3+6{)}^2}{3}$.
4. Multiply the result from the third step by 4: $\left(\frac{(3+6{)}^2}{3}\right)\times 4$.
5. Set the expression equal to $-54x$ and solve for $x$.

Key Concepts

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the given equation, correctly applying these rules is essential to simplify the expression before solving for the variable.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This typically requires isolating the variable on one side of the equation through various algebraic manipulations, such as adding, subtracting, multiplying, or dividing both sides by the same number. Understanding how to manipulate equations is crucial for arriving at the correct solution.

Negative Numbers and Their Properties

Negative numbers are values less than zero and have unique properties, especially when it comes to multiplication and division. For instance, multiplying or dividing two negative numbers results in a positive number, while multiplying or dividing a negative number by a positive number yields a negative result. Recognizing how these properties affect the outcome of the equation is vital for solving it correctly.