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Chapter 2: Problem 40

Determine whether the given number is a solution of the equation. $$x-7=2 ; 9$$

Short Answer

Expert verified
Yes, the number 9 is a solution to the equation \(x-7=2\).

Step by step solution

01

Identify the Given Elements

The given equation is \(x-7 = 2\), and the number provided for evaluation is 9.
02

Substituting the Given Number

Substitute 9 for x in the equation to find out if this number is a solution. So the equation becomes \(9 - 7 = 2\).
03

Evaluate the Equality

By performing the operation on the left side, obtain that \(2 = 2\). Since both sides of the equation are equal, the number 9 is a solution for the equation \(x - 7 = 2\).

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Key Concepts

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

Substitution Method
The substitution method is a cornerstone strategy used in algebra, especially when we're dealing with linear equations. This method involves replacing the variable in the equation with a given number or expression to solve for the variable or to evaluate if the given number is a solution to the equation.

For instance, take the linear equation from our exercise, \( x - 7 = 2 \). To determine if 9 is a solution, you substitute 9 for every x in the equation, resulting in \( 9 - 7 \). Simplify it down to \( 2 \), and since it equals the right side of the equation, 9 is indeed a solution.

In essence, the substitution method allows us to '\

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