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Chapter 2: Problem 8

Solve the equations by using the addition property. $$-21=x-9$$

Short Answer

Expert verified
The value of \( x \) is \(-12\).

Step by step solution

01

Identify the Objective

The goal of this exercise is to find the value of the variable \( x \) in the equation \(-21 = x - 9\) using the addition property of equality.
02

Isolate the Variable

To solve for \( x \), we want to get \( x \) by itself on one side of the equation. Since \( x - 9 \) is on the right side, we can add 9 to both sides of the equation to eliminate the \(-9\) from the right side.
03

Apply the Addition Property

Add 9 to both sides of the equation:\[ -21 + 9 = x - 9 + 9 \]This simplifies to:\[ -12 = x \]
04

State the Solution

The equation \(-21 = x - 9\) simplifies to \(-12 = x\), meaning the value of \( x \) is \(-12\).

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Key Concepts

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

Equation Solving
Equation solving is a fundamental skill in algebra. It involves finding the value of a variable that makes an equation true. In the given equation \(-21 = x - 9\), our task is to determine the value of \(x\) that satisfies the equation. When we solve equations, we often utilize properties of equality to maintain balance. These properties allow us to perform operations on both sides without altering the equality. The addition property is one such tool, which aids in simplifying and solving equations efficiently.
Isolate the Variable
Isolating the variable is a crucial step in solving any algebraic equation. In order to solve for \(x\) in an equation like \(-21 = x - 9\), we need to get \(x\) by itself on one side of the equation. This means removing any numbers or terms attached to \(x\).
  • We look at the equation and identify the term that needs to be moved away from the variable 鈥� in this case, \-9\.
  • By adding 9 to both sides, we effectively "cancel it out" on the side with \(x\), leaving us with \(x\) on its own.
Using techniques like this helps pave the way to simpler forms of an equation, which makes solving for the variable more straightforward.
Steps in Algebra
The process of solving equations can be broken down into clear, logical steps. These steps ensure that you address each part of the equation properly:
  • Identify the Objective: Understand what you need to find 鈥� the value of the variable.
  • Isolate the Variable: Use operations like addition or subtraction to move terms around and focus on the variable.
  • Apply the Property: Apply the addition property by adding the same value to both sides, keeping the equation balanced.
  • Simplify & Solve: Carry out the calculations to find the variable's value.
  • Check Your Solution: Always double-check by substituting the variable's value back into the original equation to verify that it holds true.
This structured approach helps tackle various algebraic problems more effectively and consistently.

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Most popular questions from this chapter

Solve the equations. More than one step is needed in each case.$$-4-6 x=44$$

Consider the formula $$\frac{x-50}{\frac{s}{\sqrt{n}}}$$ Evaluate this expression using the given values. Round the results to two decimal places. $$x=60.2, s=4.7, n=39$$

Simplify the expressions, which involve exponents and square roots. Round the results to two decimal places as necessary. $$\frac{2.026}{\sqrt{17}}$$

Use the formula for the surface area of a right circular cone given by $$ A=\pi r(r+\sqrt{h^{2}+r^{2}}) $$ where \(r\) is the radius of the base and \(h\) is the height. The surface area is in square units. Round the results to three decimal places and include proper units. The standard ice cream sugar cone has a radius of 0.937 inch and a height of 4.625 inches. What is its surface area?

Solve the equations by using the multiplication property. $$\frac{x}{4}=7$$
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