Select The Values That Make The Inequality \[$-g \ \textless \ -8\$\] True. Then Write An Equivalent Inequality In Terms Of \[$g\$\].(Numbers Written In Order From Least To Greatest Going Across.)-13, -9, -8.1, -8, -7.9, -7, -3, 0, 3,
Introduction to Inequalities
In mathematics, inequalities are used to compare two values or expressions. They are an essential part of algebra and are used to solve a wide range of problems. In this article, we will focus on solving inequalities involving the variable g. We will learn how to select the values that make an inequality true and write an equivalent inequality in terms of g.
Understanding the Given Inequality
The given inequality is . This means that the value of -g is less than -8. To solve this inequality, we need to isolate the variable g.
Isolating the Variable g
To isolate the variable g, we need to get rid of the negative sign in front of g. We can do this by multiplying both sides of the inequality by -1. However, when we multiply or divide both sides of an inequality by a negative number, we need to reverse the direction of the inequality sign.
Multiplying Both Sides by -1
Multiplying both sides of the inequality by -1 gives us:
[-(-g) \ \textgreater \ -(-8)$
This simplifies to:
[g \ \textgreater \ 8$
Understanding the Equivalent Inequality
The equivalent inequality in terms of g is [g \ \textgreater \ 8$. This means that the value of g is greater than 8.
Selecting Values that Make the Inequality True
To select the values that make the inequality true, we need to find the values of g that are greater than 8. Looking at the given list of numbers, we can see that the values that make the inequality true are:
- 3
- 0
- -3
- -7
- -7.9
- -8.1
- -8
- -9
- -13
Conclusion
In conclusion, we have learned how to solve the inequality [-g \ \textless \ -8$. We isolated the variable g by multiplying both sides of the inequality by -1 and reversed the direction of the inequality sign. We then found the equivalent inequality in terms of g, which is [g \ \textgreater \ 8$. Finally, we selected the values that make the inequality true from the given list of numbers.
Frequently Asked Questions
Q: What is an inequality?
A: An inequality is a statement that compares two values or expressions using a comparison operator such as <, >, ≤, or ≥.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable by performing the same operations on both sides of the inequality.
Q: What is the difference between an inequality and an equation?
A: An equation is a statement that says two values or expressions are equal, while an inequality is a statement that compares two values or expressions using a comparison operator.
Tips and Tricks
Tip 1: Always read the inequality carefully and understand what it is saying.
Tip 2: Isolate the variable by performing the same operations on both sides of the inequality.
Tip 3: Reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number.
Real-World Applications
Inequalities are used in a wide range of real-world applications, including:
- Finance: Inequalities are used to calculate interest rates and investment returns.
- Science: Inequalities are used to model population growth and decay.
- Engineering: Inequalities are used to design and optimize systems.
Conclusion
In conclusion, solving inequalities is an essential part of mathematics and has many real-world applications. By understanding how to solve inequalities, we can make informed decisions and solve complex problems.
Introduction
In our previous article, we discussed how to solve inequalities involving the variable g. We learned how to isolate the variable g, find the equivalent inequality in terms of g, and select the values that make the inequality true. In this article, we will provide a Q&A guide to help you better understand how to solve inequalities.
Q&A Guide
Q: What is an inequality?
A: An inequality is a statement that compares two values or expressions using a comparison operator such as <, >, ≤, or ≥.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable by performing the same operations on both sides of the inequality.
Q: What is the difference between an inequality and an equation?
A: An equation is a statement that says two values or expressions are equal, while an inequality is a statement that compares two values or expressions using a comparison operator.
Q: How do I know which direction to reverse the inequality sign?
A: When multiplying or dividing both sides of an inequality by a negative number, you need to reverse the direction of the inequality sign.
Q: Can I add or subtract the same value from both sides of an inequality?
A: Yes, you can add or subtract the same value from both sides of an inequality, but you need to make sure that the value is not negative.
Q: Can I multiply or divide both sides of an inequality by a fraction?
A: Yes, you can multiply or divide both sides of an inequality by a fraction, but you need to make sure that the fraction is not negative.
Q: How do I solve an inequality with multiple variables?
A: To solve an inequality with multiple variables, you need to isolate one variable at a time by performing the same operations on both sides of the inequality.
Q: Can I use the same method to solve an inequality with absolute value?
A: Yes, you can use the same method to solve an inequality with absolute value, but you need to consider the two cases when the expression inside the absolute value is positive or negative.
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 and then shade the region to the left or right of the point.
Q: Can I use a calculator to solve an inequality?
A: Yes, you can use a calculator to solve an inequality, but you need to make sure that the calculator is set to the correct mode and that you are using the correct operations.
Tips and Tricks
Tip 1: Always read the inequality carefully and understand what it is saying.
Tip 2: Isolate the variable by performing the same operations on both sides of the inequality.
Tip 3: Reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number.
Tip 4: Use a number line to graph an inequality and visualize the solution.
Tip 5: Check your solution by plugging it back into the original inequality.
Real-World Applications
Inequalities are used in a wide range of real-world applications, including:
- Finance: Inequalities are used to calculate interest rates and investment returns.
- Science: Inequalities are used to model population growth and decay.
- Engineering: Inequalities are used to design and optimize systems.
Conclusion
In conclusion, solving inequalities is an essential part of mathematics and has many real-world applications. By understanding how to solve inequalities, we can make informed decisions and solve complex problems. We hope that this Q&A guide has helped you better understand how to solve inequalities and has provided you with the tools and confidence to tackle more complex problems.
Frequently Asked Questions
Q: What is the difference between a linear inequality and a quadratic inequality?
A: A linear inequality is an inequality that can be written in the form ax + b < c, while a quadratic inequality is an inequality that can be written in the form ax^2 + bx + c < 0.
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 sign of the expression to determine the solution.
Q: Can I use the quadratic formula to solve a quadratic inequality?
A: Yes, you can use the quadratic formula to solve a quadratic inequality, but you need to make sure that the formula is used correctly and that the solution is checked.
Q: How do I graph a quadratic inequality on a number line?
A: To graph a quadratic inequality on a number line, you need to plot a point on the number line that represents the solution to the inequality and then shade the region to the left or right of the point.
Q: Can I use a calculator to solve a quadratic inequality?
A: Yes, you can use a calculator to solve a quadratic inequality, but you need to make sure that the calculator is set to the correct mode and that you are using the correct operations.