Solve Each Equation:1. $a - 2.01 = 5.5$2. $b + 2.01 = 5.5$3. $10c = 13.71$4. $100d = 13.71$

Introduction

Equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving four different equations, each with a unique variable and coefficient. We will use algebraic methods to isolate the variable and find its value.

Equation 1: Solving for a

The first equation is:

$a - 2.01 = 5.5$

To solve for $a$, we need to isolate the variable on one side of the equation. We can do this by adding 2.01 to both sides of the equation.

Step 1: Add 2.01 to both sides of the equation.

$a - 2.01 + 2.01 = 5.5 + 2.01$

This simplifies to:

$a = 7.51$

Therefore, the value of $a$ is 7.51.

Equation 2: Solving for b

The second equation is:

$b + 2.01 = 5.5$

To solve for $b$, we need to isolate the variable on one side of the equation. We can do this by subtracting 2.01 from both sides of the equation.

Step 1: Subtract 2.01 from both sides of the equation.

$b + 2.01 - 2.01 = 5.5 - 2.01$

This simplifies to:

$b = 3.49$

Therefore, the value of $b$ is 3.49.

Equation 3: Solving for c

The third equation is:

$10c = 13.71$

To solve for $c$, we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by 10.

Step 1: Divide both sides of the equation by 10.

$\frac{10c}{10} = \frac{13.71}{10}$

This simplifies to:

$c = 1.371$

Therefore, the value of $c$ is 1.371.

Equation 4: Solving for d

The fourth equation is:

$100d = 13.71$

To solve for $d$, we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by 100.

Step 1: Divide both sides of the equation by 100.

$\frac{100d}{100} = \frac{13.71}{100}$

This simplifies to:

$d = 0.1371$

Therefore, the value of $d$ is 0.1371.

Conclusion

In this article, we solved four different equations using algebraic methods. We isolated the variable on one side of the equation and found its value. The equations were:

1. $a - 2.01 = 5.5$
2. $b + 2.01 = 5.5$
3. $10c = 13.71$
4. $100d = 13.71$

We found the values of $a$, $b$, $c$, and $d$ to be 7.51, 3.49, 1.371, and 0.1371, respectively.

Frequently Asked Questions

• What is the difference between an equation and an expression? An equation is a statement that two expressions are equal, while an expression is a combination of variables and constants.
• How do I solve an equation with a variable on both sides? To solve an equation with a variable on both sides, you need to isolate the variable on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation.
• What is the order of operations in algebra? The order of operations in algebra is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

References

• Algebraic Methods for Solving Equations
• Solving Equations with Variables on Both Sides
• Order of Operations in Algebra
  Solving Equations: A Q&A Guide =====================================

Introduction

Solving equations is a fundamental concept in mathematics, and it's essential to understand the basics to tackle more complex problems. In this article, we'll answer some frequently asked questions about solving equations, covering topics such as algebraic methods, variables, and order of operations.

Q&A

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

A: An equation is a statement that two expressions are equal, while an expression is a combination of variables and constants.

Example: The equation $2x + 3 = 5$ is a statement that the expression $2x + 3$ is equal to the expression $5$. On the other hand, the expression $2x + 3$ is a combination of variables and constants.

Q: How do I solve an equation with a variable on both sides?

A: To solve an equation with a variable on both sides, you need to isolate the variable on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation.

Example: To solve the equation $x + 2 = 5$, you can subtract 2 from both sides to get $x = 3$.

Q: What is the order of operations in algebra?

A: The order of operations in algebra is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Example: When evaluating the expression $3 \times 2 + 4^2$, you would follow the order of operations as follows:

1. Evaluate the exponent: $4^2 = 16$
2. Multiply 3 and 2: $3 \times 2 = 6$
3. Add 6 and 16: $6 + 16 = 22$

Q: How do I solve an equation with fractions?

A: To solve an equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Example: To solve the equation $\frac{x}{2} = 3$, you can multiply both sides by 2 to get $x = 6$.

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

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Example: The equation $2x + 3 = 5$ is a linear equation, while the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.

Q: How do I solve a system of equations?

A: To solve a system of equations, you need to find the values of the variables that satisfy both equations. You can do this by using substitution or elimination methods.

Example: To solve the system of equations $x + y = 3$ and $x - y = 1$, you can add the two equations to get $2x = 4$, and then divide both sides by 2 to get $x = 2$. You can then substitute $x = 2$ into one of the original equations to get $y = 1$.

Conclusion

Solving equations is a fundamental concept in mathematics, and it's essential to understand the basics to tackle more complex problems. In this article, we've answered some frequently asked questions about solving equations, covering topics such as algebraic methods, variables, and order of operations. We hope this guide has been helpful in clarifying any doubts you may have had about solving equations.

Frequently Asked Questions

• What is the difference between an equation and an expression? An equation is a statement that two expressions are equal, while an expression is a combination of variables and constants.
• How do I solve an equation with a variable on both sides? To solve an equation with a variable on both sides, you need to isolate the variable on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation.
• What is the order of operations in algebra? The order of operations in algebra is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

References

• Algebraic Methods for Solving Equations
• Solving Equations with Variables on Both Sides
• Order of Operations in Algebra