/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 60 \(3-8 x=-9 x-1\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 60

\(3-8 x=-9 x-1\)

Short Answer

Expert verified
x = -4

Step by step solution

01

Simplify Both Sides

Start by simplifying both sides of the equation if needed. In this case, both sides are already simplified: - Left side: 3 - 8x - Right side: -9x - 1
02

Move Variable Terms to One Side

Add 9x to both sides of the equation to get all variable terms on one side: 3 - 8x + 9x = -9x - 1 + 9xThis simplifies to: 3 + x = -1
03

Solve for the Variable

Next, isolate the variable term by subtracting 3 from both sides:3 + x - 3 = -1 - 3This simplifies to:x = -4

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

solving equations
Solving equations involves finding the value of the variable that makes the equation true. In the given exercise, we are working with a linear equation, which is an equation where the highest power of the variable is one. The steps to solve linear equations often involve simplifying both sides, moving variable terms to one side, and isolating the variable. Always check that your final answer satisfies the original equation. This way, you verify correctness and ensure the solution you found is accurate.
algebraic manipulation
Algebraic manipulation is the process of using algebraic methods to simplify or rearrange expressions. In our exercise, we start by simplifying both sides. Simplification often includes combining like terms or simplifying constants. Here, both sides are already in their simplest form: 3 - 8x on the left and -9x - 1 on the right.
Moving on, we added 9x to both sides to collect all variable terms on one side of the equation:
  • Original: 3 - 8x = -9x - 1
  • Adding 9x to both sides: 3 - 8x + 9x = -9x - 1 + 9x
  • Resulting in: 3 + x = -1
Here, adding 9x to both sides utilized the property of equality, ensuring the equation remains balanced while we rearrange it for easier solving.
variable isolation
Variable isolation means to get the variable by itself on one side of the equation. This process typically involves using inverse operations to 'undo' addition, subtraction, multiplication, or division around the variable. In our exercise, after moving variable terms to one side, we have the equation 3 + x = -1.
Next, we isolate the variable x by subtracting 3 from both sides of the equation:
  • Equation: 3 + x = -1
  • Subtracting 3 from both sides: 3 + x - 3 = -1 - 3
  • Simplifies to: x = -4
By isolating the variable, we determine the value that satisfies the original equation. Remember, your goal is to get the variable alone on one side by performing opposite operations until it is isolated.

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