Solve The Inequality $15t \ \textgreater \ 180$.$t \square$

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Introduction

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In mathematics, inequalities are a fundamental concept that helps us compare values and make decisions. Solving an inequality involves finding the values of the variable that satisfy the given inequality. In this article, we will focus on solving the inequality $15t > 180$, where $t$ is the variable.

Understanding the Inequality

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The given inequality is $15t > 180$. This means that the product of $15$ and $t$ is greater than $180$. To solve this inequality, we need to isolate the variable $t$.

Isolating the Variable

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To isolate the variable $t$, we need to get rid of the coefficient $15$ that is being multiplied by $t$. We can do this by dividing both sides of the inequality by $15$.

\frac{15t}{15} > \frac{180}{15}

Simplifying the Inequality

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After dividing both sides of the inequality by $15$, we get:

t > 12

This means that the value of $t$ must be greater than $12$ to satisfy the given inequality.

Solving the Inequality: A Step-by-Step Guide

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Now that we have isolated the variable $t$, let's go through the steps to solve the inequality:

Step 1: Write Down the Inequality

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The given inequality is $15t > 180$.

Step 2: Isolate the Variable

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To isolate the variable $t$, we need to get rid of the coefficient $15$ that is being multiplied by $t$. We can do this by dividing both sides of the inequality by $15$.

\frac{15t}{15} > \frac{180}{15}

Step 3: Simplify the Inequality

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After dividing both sides of the inequality by $15$, we get:

t > 12

This means that the value of $t$ must be greater than $12$ to satisfy the given inequality.

Conclusion

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Solving an inequality involves finding the values of the variable that satisfy the given inequality. In this article, we solved the inequality $15t > 180$ by isolating the variable $t$ and simplifying the inequality. We found that the value of $t$ must be greater than $12$ to satisfy the given inequality.

Frequently Asked Questions

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Q: What is an inequality?

A: An inequality is a statement that compares two values using a mathematical symbol such as $>$, $<$, $\geq$, or $\leq$.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable and simplify the inequality.

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.

Example Problems

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Problem 1: Solve the inequality $2x > 10$

To solve this inequality, we need to isolate the variable $x$ by dividing both sides of the inequality by $2$.

\frac{2x}{2} > \frac{10}{2}

This simplifies to:

x > 5

Problem 2: Solve the inequality $x < 8$

To solve this inequality, we need to isolate the variable $x$ by subtracting $8$ from both sides of the inequality.

x - 8 < 0

This simplifies to:

x < 8

Practice Problems

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Problem 1: Solve the inequality $3y > 15$

To solve this inequality, we need to isolate the variable $y$ by dividing both sides of the inequality by $3$.

\frac{3y}{3} > \frac{15}{3}

This simplifies to:

y > 5

Problem 2: Solve the inequality $x \geq 10$

To solve this inequality, we need to isolate the variable $x$ by subtracting $10$ from both sides of the inequality.

x - 10 \geq 0

This simplifies to:

x \geq 10

Conclusion

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Solving an inequality involves finding the values of the variable that satisfy the given inequality. In this article, we solved the inequality $15t > 180$ by isolating the variable $t$ and simplifying the inequality. We found that the value of $t$ must be greater than $12$ to satisfy the given inequality. We also provided example problems and practice problems to help you understand how to solve inequalities.

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Introduction

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In our previous article, we discussed how to solve inequalities and provided step-by-step guides and example problems to help you understand the concept. However, we know that you may still have some questions about inequalities. In this article, we will address some of the most frequently asked questions about inequalities and provide answers to help you better understand the concept.

Q&A: Inequality Basics

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Q: What is an inequality?

A: An inequality is a statement that compares two values using a mathematical symbol such as $>$, $<$, $\geq$, or $\leq$.

Q: How do I know which inequality symbol to use?

A: The inequality symbol you use depends on the relationship between the two values being compared. For example, if you are comparing two values and one is greater than the other, you would use the $>$ symbol.

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.

Q&A: Solving Inequalities

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Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable and simplify the inequality.

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

A: The first step in solving an inequality is to isolate the variable by getting rid of any constants or coefficients that are being multiplied by the variable.

Q: How do I isolate the variable in an inequality?

A: To isolate the variable in an inequality, you can use inverse operations such as addition, subtraction, multiplication, or division to get rid of any constants or coefficients that are being multiplied by the variable.

Q&A: Inequality Symbols

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Q: What does the $>$ symbol mean in an inequality?

A: The $>$ symbol means that the value on the left side of the inequality is greater than the value on the right side.

Q: What does the $<$ symbol mean in an inequality?

A: The $<$ symbol means that the value on the left side of the inequality is less than the value on the right side.

Q: What does the $\geq$ symbol mean in an inequality?

A: The $\geq$ symbol means that the value on the left side of the inequality is greater than or equal to the value on the right side.

Q: What does the $\leq$ symbol mean in an inequality?

A: The $\leq$ symbol means that the value on the left side of the inequality is less than or equal to the value on the right side.

Q&A: Inequality Examples

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Q: Solve the inequality $2x > 10$.

A: To solve this inequality, we need to isolate the variable $x$ by dividing both sides of the inequality by $2$.

\frac{2x}{2} > \frac{10}{2}

This simplifies to:

x > 5

Q: Solve the inequality $x < 8$.

A: To solve this inequality, we need to isolate the variable $x$ by subtracting $8$ from both sides of the inequality.

x - 8 < 0

This simplifies to:

x < 8

Q&A: Inequality Practice

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Q: Solve the inequality $3y > 15$.

A: To solve this inequality, we need to isolate the variable $y$ by dividing both sides of the inequality by $3$.

\frac{3y}{3} > \frac{15}{3}

This simplifies to:

y > 5

Q: Solve the inequality $x \geq 10$.

A: To solve this inequality, we need to isolate the variable $x$ by subtracting $10$ from both sides of the inequality.

x - 10 \geq 0

This simplifies to:

x \geq 10

Conclusion

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In this article, we addressed some of the most frequently asked questions about inequalities and provided answers to help you better understand the concept. We covered topics such as inequality basics, solving inequalities, inequality symbols, and inequality examples. We hope that this article has been helpful in clarifying any questions you may have had about inequalities.