Solve The Inequality:${ G + 2 - 2(g - 16) \ \textgreater \ 0 }$A. { G \ \textless \ 34 $}$B. { G \ \textgreater \ -30 $}$C. { G \ \textless \ -30 $}$D. { G \ \textgreater \ 34 $}$

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Introduction

In this article, we will delve into the world of inequalities and learn how to solve them. Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to symbols. Solving an inequality involves finding the values of the variable that make the inequality true. In this case, we will focus on solving the inequality g+2−2(g−16)>0g + 2 - 2(g - 16) > 0.

Understanding the Inequality

The given inequality is g+2−2(g−16)>0g + 2 - 2(g - 16) > 0. To solve this inequality, we need to simplify the expression and isolate the variable gg. Let's start by simplifying the expression inside the parentheses.

Simplifying the Expression

We can simplify the expression g−16g - 16 by distributing the negative sign:

g−16=−16g+16g - 16 = -16g + 16

Now, let's substitute this expression back into the original inequality:

g+2−2(−16g+16)>0g + 2 - 2(-16g + 16) > 0

Next, let's simplify the expression by distributing the negative sign and combining like terms:

g+2+32g−32>0g + 2 + 32g - 32 > 0

Combine like terms:

33g−30>033g - 30 > 0

Isolating the Variable

Now that we have simplified the expression, let's isolate the variable gg by adding 30 to both sides of the inequality:

33g>3033g > 30

Next, let's divide both sides of the inequality by 33:

g>3033g > \frac{30}{33}

Simplifying the Fraction

We can simplify the fraction 3033\frac{30}{33} by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

3033=1011\frac{30}{33} = \frac{10}{11}

So, the inequality becomes:

g>1011g > \frac{10}{11}

Converting the Fraction to a Decimal

We can convert the fraction 1011\frac{10}{11} to a decimal by dividing the numerator by the denominator:

1011≈0.909\frac{10}{11} \approx 0.909

So, the inequality becomes:

g>0.909g > 0.909

Comparing the Answer Choices

Now that we have solved the inequality, let's compare our answer to the answer choices:

A. g<34g < 34 B. g>−30g > -30 C. g<−30g < -30 D. g>34g > 34

Our answer is g>0.909g > 0.909, which is closest to answer choice B. g>−30g > -30.

Conclusion

In this article, we learned how to solve the inequality g+2−2(g−16)>0g + 2 - 2(g - 16) > 0. We simplified the expression, isolated the variable, and compared our answer to the answer choices. The correct answer is B. g>−30g > -30.

Frequently Asked Questions

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values using greater than, less than, greater than or equal to, or less than or equal to symbols.

Q: How do I solve an inequality?

A: To solve an inequality, you need to simplify the expression, isolate the variable, and compare your answer to the answer choices.

Q: What is the difference between an inequality and an equation?

A: An equation is a mathematical expression that states that two values are equal, while an inequality is a mathematical expression that compares two values using greater than, less than, greater than or equal to, or less than or equal to symbols.

Q: Can I use the same steps to solve a system of inequalities?

A: Yes, you can use the same steps to solve a system of inequalities. However, you may need to use additional techniques, such as graphing or substitution, to solve the system.

Final Answer

The final answer is B. g>−30g > -30.

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Introduction

In our previous article, we learned how to solve the inequality g+2−2(g−16)>0g + 2 - 2(g - 16) > 0. We simplified the expression, isolated the variable, and compared our answer to the answer choices. In this article, we will answer some frequently asked questions about solving inequalities.

Q&A

Q: What is the first step in solving an inequality?

A: The first step in solving an inequality is to simplify the expression by combining like terms and eliminating any parentheses.

Q: How do I know which direction to move the inequality sign when I add or subtract a value from both sides?

A: When you add or subtract a value from both sides of an inequality, you can move the inequality sign in the same direction as the value you added or subtracted. For example, if you add 3 to both sides of the inequality x>2x > 2, the inequality becomes x+3>5x + 3 > 5.

Q: Can I multiply or divide both sides of an inequality by a negative number?

A: No, you cannot multiply or divide both sides of an inequality by a negative number. When you multiply or divide both sides of an inequality by a negative number, you need to reverse the direction of the inequality sign.

Q: How do I solve an inequality with a fraction?

A: To solve an inequality with a fraction, you need to multiply or divide both sides of the inequality by the denominator of the fraction. This will eliminate the fraction and allow you to solve the inequality.

Q: Can I use the same steps to solve a system of inequalities?

A: Yes, you can use the same steps to solve a system of inequalities. However, you may need to use additional techniques, such as graphing or substitution, to solve the system.

Q: How do I know which answer choice is correct?

A: To determine which answer choice is correct, you need to compare your solution to the answer choices. If your solution matches one of the answer choices, then that answer choice is correct.

Common Mistakes to Avoid

1. Not simplifying the expression

Make sure to simplify the expression by combining like terms and eliminating any parentheses.

2. Not isolating the variable

Make sure to isolate the variable by adding or subtracting a value from both sides of the inequality.

3. Not reversing the direction of the inequality sign

Make sure to reverse the direction of the inequality sign when you multiply or divide both sides of the inequality by a negative number.

4. Not checking the answer choices

Make sure to compare your solution to the answer choices to determine which answer choice is correct.

Conclusion

In this article, we answered some frequently asked questions about solving inequalities. We covered topics such as simplifying the expression, isolating the variable, and reversing the direction of the inequality sign. We also discussed common mistakes to avoid when solving inequalities.

Final Tips

1. Practice, practice, practice

The more you practice solving inequalities, the more comfortable you will become with the steps and techniques involved.

2. Use online resources

There are many online resources available that can help you learn how to solve inequalities, including video tutorials and practice problems.

3. Ask for help

If you are struggling with a particular inequality or concept, don't be afraid to ask for help. You can ask a teacher, tutor, or classmate for assistance.

Final Answer

The final answer is B. g>−30g > -30.