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Chapter 3: Problem 318

In the following exercises, translate and solve. Nine more than m is equal to 5.

Short Answer

Expert verified
m = -4

Step by step solution

01

Identify the Variables

Identify what the problem is asking for. In this case, you need to find the value of the variable 'm'.
02

Translate the Words into an Equation

Take the phrase 'Nine more than m is equal to 5' and translate it into a mathematical equation. 'Nine more than' translates to 'm + 9' and 'is equal to' translates to '='. Therefore, the equation is: \[ m + 9 = 5 \]
03

Isolate the Variable

To find the value of 'm', isolate 'm' on one side of the equation. Subtract 9 from both sides of the equation:\[ m + 9 - 9 = 5 - 9 \]Simplify to get:\[ m = -4 \]
04

Verify the Solution

Double-check your solution by substituting 'm' back into the original phrase to verify.\[ 9 + (-4) = 5 \]Since this statement is true, the solution is correct.

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Key Concepts

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

identify variables
Variables are essential in mathematical problem-solving. In our problem, the variable is the unknown value we need to find. Here, the phrase 'Nine more than m is equal to 5' indicates that 'm' is the unknown we need to solve for. Recognizing variables is crucial as it helps us understand what part of the problem needs a solution. In this case, 'm' stands for the number we are looking to determine.
translate words into equations
Translating words into equations involves converting a verbal statement into a mathematical one. This process is like turning a story into a math puzzle. In our example, the phrase 'Nine more than m is equal to 5' needs to be translated. 'Nine more than' means we add 9 to 'm'. 'Is equal to' means '='. So, the sentence 'Nine more than m is equal to 5' converts to the equation:
isolate the variable
Isolating the variable is a key step in solving equations. This means getting the variable on one side of the equation by itself. For our equation, m + 9 = 5 we need to move 9 to the other side. Do this by subtracting 9 from both sides: m + 9 - 9 = 5 - 9 Simplifying the equation, we get: m = -4 This means we have isolated 'm' and found that it equals -4. Isolating the variable helps us find the solution to the problem.
verify solution
Verifying the solution ensures that our answer is correct. To do this, substitute the value of 'm' back into the original equation. Our original phrase was 'Nine more than m is equal to 5'. We found that m = -4. Substitute -4 for m: 9 + (-4) = 5 Since this statement is true, our solution is correct. Verification is essential because it helps confirm that our calculations and reasoning are accurate. Always double-check your work to avoid mistakes.

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Most popular questions from this chapter

In the following exercises, translate each phrase into an algebraic expression and then simplify. 6 more than the sum of -1 and -12

In the following exercises, locate and label the integer on the number line. $$ -3 $$

Explain why the difference of 9 and \(-6\) is 15

In the following exercises, divide. $$ 56 \div(-8) $$

In the following exercises, simplify each expression. $$-(6-8)-(2-4)$$
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