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Chapter 3: Problem 17

Solve each equation. Check your solution and graph it on a number line. $$k-6=13$$

Short Answer

Expert verified
The solution is \(k = 19\).

Step by step solution

01

Isolate the variable

Start by adding 6 to both sides of the equation to isolate the variable \(k\).\[ k - 6 + 6 = 13 + 6 \] This simplifies to:\[ k = 19 \]
02

Check the solution

To ensure the solution is correct, substitute \(k = 19\) back into the original equation. \[ 19 - 6 = 13 \] Since both sides of the equation are equal, \(k = 19\) is the correct solution.
03

Graph on a number line

To graph \(k = 19\) on a number line, draw a number line and place a point at 19. You can create a simple line with numbers and mark the 19th position clearly, indicating that is where the solution lies. Ensure that values like 18 and 20 are visible on either side of 19 for reference.

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Key Concepts

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

Isolate the Variable
To solve an equation, one of the first and most crucial steps is to isolate the variable. This means you want to get the variable all by itself on one side of the equation, usually the left side. When you isolate the variable, you're essentially unraveling the equation to find out what that variable equals.
Here's how you do it:
  • Identify the operations being performed on the variable, such as addition, subtraction, multiplication, or division.
  • Use inverse operations to cancel those out. In the case of the equation given, \(k - 6 = 13\), subtraction was used, so you'll apply addition.
  • Apply these operations equally to both sides of the equation. This keeps the equation balanced.
For example, adding 6 to both sides of \(k - 6 = 13\) simplifies it to \(k = 19\). Now, the variable \(k\) is isolated, revealing its value.
Checking Solutions
Once you've solved an equation by finding the variable's value, it's essential to check your work. This helps you verify that your solution is correct and no mistakes were made during the equation-solving process.
Here's how to check the solution:
  • Take the value you found for the variable, in this case, \(k = 19\).
  • Substitute this value back into the original equation.
  • Perform the operations to see if both sides of the equation remain equal.
For the given problem:- Substitute \(19\) for \(k\) in \(k - 6 = 13\).- Calculate \(19 - 6\) and verify that it indeed equals 13.
If both sides match, your solution is correct! This step is crucial and provides confidence that the variable's value truly satisfies the equation.
Graphing on a Number Line
Graphing the solution on a number line offers a visual representation that can make understanding the solution more intuitive. Even if drawing isn't necessary for all math problems, it can be beneficial.
Here's how to graph a solution:
  • Draw a horizontal line and mark it with evenly spaced numbers.
  • Identify where your solution falls on this line. In the exercise, this would be \(k = 19\).
  • Place a clear point or dot on the number line at 19 to indicate the position of your solution.
For additional clarity:- Make sure neighboring numbers, like 18 and 20, are also labeled. This provides context and ensures viewers though know where 19 is.
Graphing helps solidify your understanding of the solution and offers a practical way to visualize mathematical concepts.

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Most popular questions from this chapter

An electrician charges \(\$ 35\) for a house call and \(\$ 80\) per hour for each hour worked. If the total charge was \(\$ 915\) to wire a new house, which equation would you use to find the number of hours \(n\) that the electrician worked? A \(35 n+2 n(80)=915\) B \(80+35 n=915\) C \(35+(80-n)=915\) D\( 35+80 n=915\)

Use the Distributive Property to write each expression as an equivalent algebraic expression. $$2(x+y)$$

Find the next term in the pattern. $$20,22,26,32, \dots$$

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