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Chapter 1: Problem 17

Solve. Be sure to check. $$ 10+x=89 $$

Short Answer

Expert verified
x = 79

Step by step solution

01

- Isolate the Variable

To solve for x, you need to isolate the variable on one side of the equation. The equation is given as: 10 + x = 89 Subtract 10 from both sides to isolate x. This will give you: x = 89 - 10
02

- Perform the Calculation

Now, perform the subtraction on the right side of the equation: x = 89 - 10 x = 79
03

- Check the Solution

To ensure that the solution is correct, substitute x back into the original equation and verify: 10 + x = 89 10 + 79 = 89 Since both sides of the equation balance, the solution is correct.

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Key Concepts

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

Isolating Variables
When solving linear equations, the goal is often to find the value of the unknown variable. This process is known as isolating the variable. In the equation given, 10 + x = 89, our unknown variable is x. To isolate x, we need to get it alone on one side of the equation. This means we have to move all other numbers to the opposite side. In this example, we subtract 10 from both sides. By doing this, we follow the principle of keeping the equation balanced. So, the equation 10 + x = 89 becomes:

Step 1: Subtract 10 from both sides
10 + x - 10 = 89 - 10.
Simplifies to:
x = 79.

Now, we have isolated x and found that x = 79.
Subtraction
Subtraction is a key operation in solving linear equations, especially when isolating variables. In our exercise, we used subtraction to move the constant term from one side of the equation to the other. In the example 10 + x = 89:
  • First, identify the constant term that needs to be removed (which is 10 in this case).
  • Subtract this term from both sides of the equation: 10 + x - 10 = 89 - 10.
  • This simplifies to x = 79, effectively isolating the variable.

When you subtract the same number from both sides, you maintain the balance of the equation. This is crucial because it ensures the equality holds true throughout the process. Subtraction helps to simplify the equation and isolate the variable in question.
Checking Solutions
After solving for the variable, it's important to check your solution. This helps verify that your solution is correct. To check the solution:
  • Substitute the found value back into the original equation.
  • In our case, we found x = 79.
  • Replace x in the original equation with 79, making it 10 + 79 = 89.
  • Simplify to verify: 89 = 89.

Since both sides of the equation are equal, this checks out and confirms our solution. Ensuring the left-hand side equals the right-hand side after substitution proves the solution is accurate. This step is crucial for catching any possible errors made during the calculations.

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Most popular questions from this chapter

The balance in Dylan's bank account is \(\$ 749 .\) He uses his debit card for purchases of \(\$ 34\) and \(\$ 65 .\) Then he makes a deposit of \(\$ 123\) from his paycheck. What is the new balance?

Write each number in standard notation. Six hundred thirty-two thousand, eight hundred ninety-six

Estimate each quotient by first rounding to the nearest hundred. Show your work. $$ 1165 \div 236 $$

Round to the nearest ten. $$ 48 $$

Subtract. Check by adding. $$ 981-747 $$
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