Solve For \[$ B \$\]: \[$-17b = -21\$\].Enter Your Answer As A Fraction.

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, −17b=−21{-17b = -21}, to find the value of the variable b{b}. We will break down the solution step by step, using clear and concise language, and provide examples to illustrate each step.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax+b=c{ax + b = c}, where a{a}, b{b}, and c{c} are constants, and x{x} is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

Solving the Linear Equation

To solve the linear equation −17b=−21{-17b = -21}, we need to isolate the variable b{b}. We can do this by performing a series of algebraic operations, such as addition, subtraction, multiplication, and division.

Step 1: Divide Both Sides by -17

The first step in solving the equation is to divide both sides by -17. This will isolate the variable b{b} on one side of the equation.

-17b = -21
b = -21 / -17

Step 2: Simplify the Expression

Now that we have isolated the variable b{b}, we can simplify the expression by performing the division.

b = -21 / -17
b = 21 / 17

Step 3: Write the Answer as a Fraction

The final step is to write the answer as a fraction. In this case, the answer is already in fraction form, so we can simply write it as b=2117{b = \frac{21}{17}}.

Conclusion

Solving linear equations is an essential skill for students to master. By following the steps outlined in this article, we can solve even the most complex linear equations. Remember to always isolate the variable on one side of the equation, and simplify the expression by performing the necessary algebraic operations. With practice and patience, you will become proficient in solving linear equations in no time.

Frequently Asked Questions

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation by performing a series of algebraic operations, such as addition, subtraction, multiplication, and division.

Q: What is the final answer to the equation −17b=−21{-17b = -21}?

A: The final answer to the equation −17b=−21{-17b = -21} is b=2117{b = \frac{21}{17}}.

Additional Resources

For more information on solving linear equations, check out the following resources:

  • Khan Academy: Solving Linear Equations
  • Mathway: Solving Linear Equations
  • Wolfram Alpha: Solving Linear Equations

By following the steps outlined in this article and practicing with real-world examples, you will become proficient in solving linear equations in no time. Happy solving!

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Introduction

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the basics to excel in various fields, including science, engineering, and economics. In our previous article, we provided a step-by-step guide on solving linear equations. However, we understand that sometimes, it's easier to learn through questions and answers. In this article, we'll address some of the most frequently asked questions about solving linear equations.

Q&A: Solving Linear Equations

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form ax+b=c{ax + b = c}, where a{a}, b{b}, and c{c} are constants, and x{x} is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation by performing a series of algebraic operations, such as addition, subtraction, multiplication, and division.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation has the highest power of the variable(s) as 1, whereas a quadratic equation has the highest power of the variable(s) as 2. For example, 2x+3=5{2x + 3 = 5} is a linear equation, while x2+4x+4=0{x^2 + 4x + 4 = 0} is a quadratic equation.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to follow the same steps as solving a linear equation with integers. However, you may need to multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the underlying math to ensure that you're using the calculator correctly.

Q: How do I check my answer to a linear equation?

A: To check your answer to a linear equation, you need to plug the solution back into the original equation and verify that it's true. If the solution satisfies the equation, then it's correct.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Not isolating the variable on one side of the equation
  • Not following the order of operations (PEMDAS)
  • Not checking the solution to the equation
  • Not using the correct algebraic operations to solve the equation

Additional Resources

For more information on solving linear equations, check out the following resources:

  • Khan Academy: Solving Linear Equations
  • Mathway: Solving Linear Equations
  • Wolfram Alpha: Solving Linear Equations

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the basics to excel in various fields. By following the steps outlined in this article and practicing with real-world examples, you'll become proficient in solving linear equations in no time. Remember to always check your answer to ensure that it's correct, and don't be afraid to ask for help if you're struggling.

Frequently Asked Questions (FAQs)

Q: What is the final answer to the equation −17b=−21{-17b = -21}?

A: The final answer to the equation −17b=−21{-17b = -21} is b=2117{b = \frac{21}{17}}.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, you need to follow the same steps as solving a linear equation with integers. However, you may need to multiply both sides of the equation by a power of 10 to eliminate the decimals.

Q: Can I use a graphing calculator to solve linear equations?

A: Yes, you can use a graphing calculator to solve linear equations. However, it's essential to understand the underlying math to ensure that you're using the calculator correctly.

Q: How do I solve a linear equation with absolute value?

A: To solve a linear equation with absolute value, you need to follow the same steps as solving a linear equation with integers. However, you may need to consider both the positive and negative cases of the absolute value.