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Chapter 11: Problem 23

Solve using the addition principle. $$ x-7=-21 $$

Short Answer

Expert verified
x = -14

Step by step solution

01

- Identify the Equation

The given equation to solve is: \[ x - 7 = -21 \]
02

- Apply the Addition Principle

Add 7 to both sides of the equation to isolate the variable on one side. This gives: \[ x - 7 + 7 = -21 + 7 \]
03

- Simplify Both Sides

On the left side, \( -7 + 7 = 0 \), so it simplifies to \( x \). On the right side, \( -21 + 7 = -14 \). Thus, the equation is: \[ x = -14 \]

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Key Concepts

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

linear equations
A linear equation is a type of algebraic equation in which the highest power of the variable is one. This means that the variable is not raised to any exponent higher than one. In the given example, the linear equation is \[ x - 7 = -21 \].
Linear equations have several key characteristics:
  • They graph as straight lines on a coordinate plane.
  • There is a constant rate of change between variables.
  • The solution to a linear equation is always a single value or a set of values that satisfy the equation.
Solving linear equations often requires isolating the variable, which we'll discuss in the next section.
isolating variables
Isolating the variable means rearranging the equation so that the variable stands alone on one side of the equation. This is a crucial step in solving any equation.
In the problem \[ x - 7 = -21 \], our goal is to get \( x \) by itself. Here鈥檚 a simple way to think about it:
  • Identify what is being done to the variable \( x \). In this case, \( 7 \) is being subtracted.
  • Use the opposite operation to cancel it out. Since 7 is subtracted, we add 7 to both sides of the equation:
\[ x - 7 + 7 = -21 + 7 \]
This leads us to our final topic, solving for \( x \).
solving for x
Once we have isolated the variable, we need to simplify both sides to find the value of \( x \).
From the previous step, we have:
  • \( x - 7 + 7 = -21 + 7 \)

On the left side of the equation, \(-7 + 7 = 0\), so we are left with \( x \).
On the right side, we calculate \(-21 + 7 = -14\).
So, the simplified equation is:
\[ x = -14 \]
This tells us that the value of \( x \) which satisfies the original equation \( x - 7 = -21 \) is \( -14 \). Remember, always double-check your work by plugging the solution back into the original equation to make sure it satisfies the equation.

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Most popular questions from this chapter

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