What Is The Value Of $a$ In The Equation $3a + B = 54$, When \$b = 9$[/tex\]?A. 15 B. 18 C. 21 D. 27

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving a linear equation with one variable, where the value of another variable is given. We will use the equation $3a + b = 54$ and find the value of $a$ when $b = 9$.

Understanding the Equation

The given equation is a linear equation in one variable, which means it has only one unknown variable, $a$. The equation is in the form $ax + b = c$, where $a$ is the coefficient of the variable, $b$ is the constant term, and $c$ is the constant on the right-hand side. In this case, the equation is $3a + b = 54$, where $a$ is the unknown variable, $b$ is the constant term, and $54$ is the constant on the right-hand side.

Substituting the Value of $b$

We are given that $b = 9$. To find the value of $a$, we need to substitute this value into the equation. This means we will replace $b$ with $9$ in the equation $3a + b = 54$.

Solving for $a$

After substituting the value of $b$, the equation becomes $3a + 9 = 54$. To solve for $a$, we need to isolate the variable $a$ on one side of the equation. We can do this by subtracting $9$ from both sides of the equation.

Subtracting $9$ from Both Sides

Subtracting $9$ from both sides of the equation gives us $3a = 54 - 9$. Simplifying the right-hand side of the equation, we get $3a = 45$.

Dividing Both Sides by $3$

To isolate the variable $a$, we need to divide both sides of the equation by $3$. This gives us $a = \frac{45}{3}$.

Simplifying the Fraction

Simplifying the fraction, we get $a = 15$.

Conclusion

In this article, we solved a linear equation with one variable, where the value of another variable was given. We used the equation $3a + b = 54$ and found the value of $a$ when $b = 9$. By substituting the value of $b$ into the equation and solving for $a$, we found that $a = 15$.

Frequently Asked Questions

  • What is the value of $a$ in the equation $3a + b = 54$, when $b = 9$?
  • How do we solve a linear equation with one variable?
  • What is the process of isolating a variable on one side of an equation?

Answers

  • The value of $a$ in the equation $3a + b = 54$, when $b = 9$, is $15$.
  • To solve a linear equation with one variable, we need to isolate the variable on one side of the equation.
  • The process of isolating a variable on one side of an equation involves adding or subtracting the same value to both sides of the equation, and then dividing both sides by the coefficient of the variable.

Final Thoughts

Solving equations is an essential skill in mathematics, and it requires practice and patience. By following the steps outlined in this article, you can solve linear equations with one variable and find the value of unknown variables. Remember to substitute the value of known variables into the equation, isolate the variable on one side of the equation, and simplify the resulting expression. With practice, you will become proficient in solving equations and applying mathematical concepts to real-world problems.

Introduction

In our previous article, we discussed how to solve a linear equation with one variable, where the value of another variable was given. We used the equation $3a + b = 54$ and found the value of $a$ when $b = 9$. In this article, we will answer some frequently asked questions about solving linear equations with one variable.

Q&A

Q: What is the first step in solving a linear equation with one variable?

A: The first step in solving a linear equation with one variable is to substitute the value of known variables into the equation.

Q: How do I isolate the variable on one side of the equation?

A: To isolate the variable on one side of the equation, you need to add or subtract the same value to both sides of the equation, and then divide both sides by the coefficient of the variable.

Q: What is the coefficient of the variable?

A: The coefficient of the variable is the number that is multiplied by the variable. In the equation $3a + b = 54$, the coefficient of the variable $a$ is $3$.

Q: How do I simplify the resulting expression?

A: To simplify the resulting expression, you need to perform the operations indicated by the signs in the equation. For example, if the equation is $3a = 45$, you can simplify it by dividing both sides by $3$, which gives you $a = 15$.

Q: What if the equation has a fraction as the coefficient of the variable?

A: If the equation has a fraction as the coefficient of the variable, you need to multiply both sides of the equation by the reciprocal of the fraction to eliminate the fraction. For example, if the equation is $\frac{1}{2}a = 12$, you can multiply both sides by $2$ to get $a = 24$.

Q: Can I use the same steps to solve a linear equation with two variables?

A: No, you cannot use the same steps to solve a linear equation with two variables. Solving a linear equation with two variables requires a different approach, such as substitution or elimination.

Q: What if the equation has a negative sign in front of the variable?

A: If the equation has a negative sign in front of the variable, you need to multiply both sides of the equation by $-1$ to eliminate the negative sign. For example, if the equation is $-3a = 54$, you can multiply both sides by $-1$ to get $3a = -54$.

Conclusion

Solving linear equations with one variable is an essential skill in mathematics, and it requires practice and patience. By following the steps outlined in this article, you can answer frequently asked questions about solving linear equations with one variable. Remember to substitute the value of known variables into the equation, isolate the variable on one side of the equation, and simplify the resulting expression.

Frequently Asked Questions

  • What is the first step in solving a linear equation with one variable?
  • How do I isolate the variable on one side of the equation?
  • What is the coefficient of the variable?
  • How do I simplify the resulting expression?
  • What if the equation has a fraction as the coefficient of the variable?
  • Can I use the same steps to solve a linear equation with two variables?
  • What if the equation has a negative sign in front of the variable?

Answers

  • The first step in solving a linear equation with one variable is to substitute the value of known variables into the equation.
  • To isolate the variable on one side of the equation, you need to add or subtract the same value to both sides of the equation, and then divide both sides by the coefficient of the variable.
  • The coefficient of the variable is the number that is multiplied by the variable.
  • To simplify the resulting expression, you need to perform the operations indicated by the signs in the equation.
  • If the equation has a fraction as the coefficient of the variable, you need to multiply both sides of the equation by the reciprocal of the fraction to eliminate the fraction.
  • No, you cannot use the same steps to solve a linear equation with two variables.
  • If the equation has a negative sign in front of the variable, you need to multiply both sides of the equation by $-1$ to eliminate the negative sign.