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

Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

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Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 99

Chapter 2, Problem 99

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

Verified step by step guidance

First, simplify the expression inside the parentheses: calculate $3 + 6$.

Next, square the result from the first step: compute $(3 + 6)^2$.

Then, divide the squared result by 3: calculate $\frac{(3 + 6)^2}{3}$.

Multiply the quotient by 4 as indicated: compute $\left(\frac{(3 + 6)^2}{3}\right) \times 4$.

Set the expression equal to $-54x$ and solve for $x$ by isolating $x$ on one side of the equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses first, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction. Correctly applying this ensures accurate simplification of expressions.

Solving Linear Equations

Solving linear equations involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, or division. The goal is to find the value of the variable that makes the equation true.

Distributive Property and Simplification

The distributive property allows you to multiply a sum by multiplying each addend separately and then adding the products. Simplifying expressions using this property helps in reducing complex expressions to simpler forms, making it easier to solve equations.

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