Work Out The Largest Whole Number \[$x\$\] Could Be So That \[$7 + X\$\] Is Larger Than \[$2x\$\].$\[ \begin{tabular}{|c|c|c|} \hline x & 7+x & 2x \\ \hline 0 & 7 & 0 \\ \hline 1 & 8 & 2 \\ \hline 2 & 9 & 4 \\ \hline 3 & 10
Introduction
In mathematics, inequalities are a fundamental concept that helps us compare values and make decisions. In this article, we will explore how to solve inequalities and find the largest whole number that satisfies a given condition. We will use a specific example to illustrate the concept and provide step-by-step solutions.
Understanding the Problem
The problem asks us to find the largest whole number {x$}$ such that ${7 + x\$} is larger than ${2x\$}. This can be represented as an inequality:
Breaking Down the Inequality
To solve this inequality, we need to isolate the variable {x$. We can start by subtracting [x\$} from both sides of the inequality:
This tells us that {x$}$ must be less than 7.
Finding the Largest Whole Number
Since {x$}$ must be a whole number, we need to find the largest whole number that is less than 7. The largest whole number less than 7 is 6.
Verifying the Solution
To verify our solution, we can plug in {x = 6$}$ into the original inequality:
This is true, so our solution is correct.
Conclusion
In this article, we solved an inequality and found the largest whole number that satisfies a given condition. We used a step-by-step approach to isolate the variable and verify our solution. This type of problem is commonly encountered in mathematics and is an essential skill to develop.
Example Solutions
Example 1
Find the largest whole number {x$}$ such that ${3 + x\$} is larger than {x$}$.
Solution
Subtracting {x$}$ from both sides:
This is true for all values of {x$, so the largest whole number is any positive integer.
Example 2
Find the largest whole number [x\$} such that ${5 + x\$} is larger than ${3x\$}.
Solution
Subtracting {x$}$ from both sides:
Dividing both sides by 2:
The largest whole number less than is 2.
Tips and Tricks
- When solving inequalities, always isolate the variable on one side of the inequality.
- Use the properties of inequalities to simplify the expression.
- Verify your solution by plugging in the value of the variable into the original inequality.
Conclusion
Introduction
In our previous article, we explored how to solve inequalities and find the largest whole number that satisfies a given condition. In this article, we will provide a Q&A guide to help you understand the concept better and answer common questions.
Q: What is an inequality?
A: An inequality is a statement that compares two values using a mathematical symbol, such as <, >, ≤, or ≥.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable on one side of the inequality. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.
Q: What is the difference between an inequality and an equation?
A: An equation is a statement that says two values are equal, while an inequality is a statement that compares two values using a mathematical symbol. For example, the equation 2x = 4 is different from the inequality 2x > 4.
Q: How do I know which direction to move the inequality symbol?
A: When you add or subtract the same value to both sides of an inequality, the direction of the inequality symbol remains the same. However, when you multiply or divide both sides of an inequality by a negative value, the direction of the inequality symbol is reversed.
Q: Can I use the same steps to solve linear inequalities and quadratic inequalities?
A: No, the steps to solve linear inequalities and quadratic inequalities are different. Linear inequalities can be solved using the same steps as linear equations, while quadratic inequalities require a different approach.
Q: How do I solve a quadratic inequality?
A: To solve a quadratic inequality, you need to factor the quadratic expression and then use the properties of inequalities to simplify the expression. You can also use the quadratic formula to find the solutions to the quadratic equation.
Q: Can I use a calculator to solve inequalities?
A: Yes, you can use a calculator to solve inequalities, but you need to make sure that the calculator is set to the correct mode and that you are using the correct operations.
Q: How do I graph an inequality on a number line?
A: To graph an inequality on a number line, you need to plot a point on the number line that represents the solution to the inequality. You can then use a closed circle to represent the solution to the inequality if the inequality is in the form of ≤ or ≥, or an open circle if the inequality is in the form of < or >.
Q: Can I use the same steps to solve inequalities with fractions and decimals?
A: Yes, the steps to solve inequalities with fractions and decimals are the same as the steps to solve inequalities with integers.
Q: How do I check my solution to an inequality?
A: To check your solution to an inequality, you need to plug in the value of the variable into the original inequality and make sure that the inequality is true.
Conclusion
In conclusion, solving inequalities is an essential skill in mathematics that helps us compare values and make decisions. By following the steps outlined in this article, you can solve inequalities and answer common questions. Remember to always verify your solution and use the properties of inequalities to simplify the expression.
Common Mistakes to Avoid
- Not isolating the variable on one side of the inequality
- Not using the correct operations when solving inequalities
- Not verifying the solution to the inequality
- Not using the properties of inequalities to simplify the expression
Tips and Tricks
- Use a number line to graph inequalities and visualize the solution
- Use a calculator to check your solution to an inequality
- Use the properties of inequalities to simplify the expression
- Verify your solution to an inequality by plugging in the value of the variable into the original inequality