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Chapter 2: Problem 26

Solve using the addition principle. Don't forget to check! $$ x-9=6 $$

Short Answer

Expert verified
The solution is \( x = 15 \).

Step by step solution

01

Understand the Equation

First, identify the given equation. Here, the equation is \( x - 9 = 6 \).
02

Isolate the Variable

To isolate \( x \), use the addition principle. Add 9 to both sides of the equation: \( x - 9 + 9 = 6 + 9 \).
03

Simplify Both Sides

Simplify the left side: \( x - 9 + 9 = x \) and the right side: \( 6 + 9 = 15 \). Thus, the simplified equation is \( x = 15 \).
04

Check the Solution

Verify the solution by substituting 15 back into the original equation: \( 15 - 9 = 6 \). Since the equation holds true, \( x = 15 \) is the correct solution.

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Key Concepts

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

solving linear equations
When solving linear equations, the primary goal is to find the value of the variable that makes the equation true. Linear equations have the general form \(ax + b = c\) where \(a\), \(b\), and \(c\) are constants. In our exercise, the equation is \(x - 9 = 6\). By solving such equations, you learn how to manipulate algebraic expressions to uncover unknown values. Knowing how to solve linear equations is fundamental for tackling more complex algebra problems in the future.
isolating variables
Isolating the variable is a key step in solving equations. The variable is the unknown part of the equation that we aim to solve for, which in our case is \(x\). To isolate \(x\) in the equation \(x - 9 = 6\), we use the addition principle. The addition principle states that you can add or subtract the same value from both sides of the equation without changing its equality. Here, adding 9 to both sides helps us get: \[x - 9 + 9 = 6 + 9\]. After performing this operation, \(x\) is isolated, giving us \[x = 15\]. Isolating variables is crucial because it simplifies the equation, making it easier to solve.
algebraic simplification
Once the variable is isolated, the next step is algebraic simplification. This involves performing arithmetic operations to simplify each side of the equation. From our previous step, we had: \[x - 9 + 9 = 6 + 9\]. Simplifying the left side gives us \(x\), and simplifying the right side results in \[15\]. So the equation \[x - 9 + 9 = 15\] simplifies to \[x = 15\]. Simplification helps reduce the equation to its most basic form, making the solution clearer and easier to understand.
equation verification
After finding the solution, it is important to verify it. Verification ensures that our solution is correct and consistent with the original equation. Substituting \(x = 15\) back into the original equation \(x - 9 = 6\) gives us: \[15 - 9 = 6\]. Since both sides equal \(6\), the solution is verified as correct. Verification is essential in algebra to confirm that the derived solution truly satisfies the given equation, providing confidence in our results.

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. In the last weeks before the yearly Topsfield Weigh In, heavyweight pumpkins gain about 26 lb per day. Charlotte's heaviest pumpkin weighs 532 lb on September \(5 .\) For what dates will its weight exceed 818 lb?

Elsa has an average score of 82 on three tests. Her average score on the first two tests is \(85 .\) What was the score on the third test?

Use an inequality and the five-step process to solve each problem. Reduced Fat Oreo " cookies contain 4.5 of fat per serving. In order for a food to be labeled "reduced fat," it must have at least \(25 \%\) less fat than the regular item. What can you conclude about the number of grams of fat in a serving of the regular Oreo cookies?

Use an inequality and the five-step process to solve each problem. An unconditional acceptance into the Master of Business Administration (MBA) program at Arkansas State University will be given to students whose GMAT score plus 200 times the undergraduate grade point average is at least \(950 .\) Chloe's GMAT score was \(500 .\) What must her grade point average be in order to be unconditionally accepted into the program?

Review operations with real numbers. Simplify. $$ \frac{1}{2} \div\left(-\frac{3}{4}\right) $$
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