Problem 81 - Algebra 1

Question

For which inequality is \(x=238\) a solution? (A) \(250 \geq x+12\) (B) \(250x+12\)

Step-by-Step Solution

Answer

The value \(x=238\) is a solution for inequality A (\(250 \geq x+12\))

Step 1: Review Individual Inequalities

Solve each inequality individually substituting x with 238. This will give the result for each equation which can then be compared with the left side of the inequality to see if the inequality holds.

Step 2: Solve First Inequality

Let's solve inequality A: \(250 \geq x+12\). We substitute \(x=238\) into A: \(250 \geq 238+12\). Simplifying, we have \(250 \geq 250\), which is true. So \(x=238\) is a solution for inequality A.

Step 3: Solve Second Inequality

Next we solve inequality B: \(250

Step 4: Solve Third Inequality

Lastly, we solve inequality C: \(250>x+12\). Substituting \(x=238\) into C gives \(250>238+12\). Simplifying, we have \(250>250\), which is also false. So \(x=238\) is not a solution for inequality C.

Key Concepts

Algebra

Algebra is all about using symbols, like letters, to represent values in mathematical expressions and equations. Think of numbers and operations like addition and subtraction as a language for numbers. In this exercise, we focus on inequalities, which are like equations but instead of saying two things are equal, they show how one quantity compares to another.
The symbols used in inequalities are as follows:

• \(\geq\) means "greater than or equal to." This symbol shows that one value is either larger than or exactly the same as the other.
• \(>\) means "greater than," indicating the value on one side is larger.
• \(<\) means "less than," which tells us that the value on one side is smaller.

Understanding these symbols and how to work with them is essential in algebra. When solving inequalities, like the ones in our exercise, substituting the given number can help evaluate if the inequality holds true.

Mathematical Reasoning

Mathematical reasoning helps us understand why and how mathematical statements, like inequalities, are true or false. It involves logical thinking to deduce conclusions based on previous statements or known truths. In our exercise, reasoning is used to check solutions:

• First, substitute the value into the inequality.
• Next, simplify the expression to see if the inequality holds true.
• Finally, compare the simplified result to the original statement.

For example, with the inequality \(250 \geq 238 + 12\), we substituted \(x = 238\) and simplified it to \(250 \geq 250\). This reasoning proves the statement holds because 250 is equal to 250, satisfying the condition for "greater than or equal to." Mathematical reasoning is crucial because it allows you to verify solutions and understand their validity in problem-solving.

Problem Solving

Problem solving in mathematics involves a series of logical steps aimed at finding a solution. You can follow these steps to approach problems with confidence:

• Read and understand the problem. This means figuring out what is being asked and what information is given.
• Choose a strategy. In the case of inequalities, this might mean substituting and simplifying values to check solutions.
• Carry out the plan by substituting values into each inequality and simplifying the results.
• Check your solution by verifying if the values satisfy the conditions of the inequality.

In this exercise, we solved each inequality by substituting \(x = 238\), then simplified to check if our results met the given conditions. Problem-solving transforms chaos into clarity by providing a structured approach to untangling mathematical questions.
This approach not only applies to inequalities but any algebraic challenges you might encounter.

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Problem 81

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Key Concepts

Algebra

Algebra is all about using symbols, like letters, to represent values in mathematical expressions and equations. Think of numbers and operations like addition and subtraction as a language for numbers. In this exercise, we focus on inequalities, which are like equations but instead of saying two things are equal, they show how one quantity compares to another.
The symbols used in inequalities are as follows:

• \(\geq\) means "greater than or equal to." This symbol shows that one value is either larger than or exactly the same as the other.
• \(>\) means "greater than," indicating the value on one side is larger.
• \(<\) means "less than," which tells us that the value on one side is smaller.

Understanding these symbols and how to work with them is essential in algebra. When solving inequalities, like the ones in our exercise, substituting the given number can help evaluate if the inequality holds true.

Mathematical Reasoning

Mathematical reasoning helps us understand why and how mathematical statements, like inequalities, are true or false. It involves logical thinking to deduce conclusions based on previous statements or known truths. In our exercise, reasoning is used to check solutions:

• First, substitute the value into the inequality.
• Next, simplify the expression to see if the inequality holds true.
• Finally, compare the simplified result to the original statement.

For example, with the inequality \(250 \geq 238 + 12\), we substituted \(x = 238\) and simplified it to \(250 \geq 250\). This reasoning proves the statement holds because 250 is equal to 250, satisfying the condition for "greater than or equal to." Mathematical reasoning is crucial because it allows you to verify solutions and understand their validity in problem-solving.

Problem Solving

Problem solving in mathematics involves a series of logical steps aimed at finding a solution. You can follow these steps to approach problems with confidence:

• Read and understand the problem. This means figuring out what is being asked and what information is given.
• Choose a strategy. In the case of inequalities, this might mean substituting and simplifying values to check solutions.
• Carry out the plan by substituting values into each inequality and simplifying the results.
• Check your solution by verifying if the values satisfy the conditions of the inequality.

In this exercise, we solved each inequality by substituting \(x = 238\), then simplified to check if our results met the given conditions. Problem-solving transforms chaos into clarity by providing a structured approach to untangling mathematical questions.
This approach not only applies to inequalities but any algebraic challenges you might encounter.