Select The Best Answer For The Question.Solve The Equation: 12 Y = 132 12y = 132 12 Y = 132 .A. Y = 144 Y = 144 Y = 144 B. Y = 11 12 Y = \frac{11}{12} Y = 12 11 C. Y = 11 Y = 11 Y = 11 D. Y = 1 11 Y = \frac{1}{11} Y = 11 1

Mar 8, 2025 by ADMIN 227 views

**Solving Linear Equations: A Step-by-Step Guide**

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, $12y = 132$ , and provide a step-by-step guide on how to arrive at the correct solution.

Understanding the Equation

The given equation is $12y = 132$ . This is a linear equation in one variable, where $y$ is the variable we need to solve for. The equation states that the product of $12$ and $y$ is equal to $132$ .

Step 1: Isolate the Variable

To solve for $y$ , we need to isolate the variable on one side of the equation. In this case, we can start by dividing both sides of the equation by $12$ . This will cancel out the $12$ on the left-hand side and leave us with $y$ on its own.

\frac{12y}{12} = \frac{132}{12}

Step 2: Simplify the Equation

After dividing both sides by $12$ , we get:

y = \frac{132}{12}

Step 3: Simplify the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is $12$ . This gives us:

y = \frac{11}{1}

Step 4: Write the Final Answer

Therefore, the final answer to the equation $12y = 132$ is:

y = 11

Conclusion

Solving linear equations is a straightforward process that involves isolating the variable and simplifying the equation. By following the steps outlined above, we can arrive at the correct solution to the equation $12y = 132$ . Remember to always check your work and make sure that the solution satisfies the original equation.

Answer Options

Now that we have solved the equation, let's take a look at the answer options provided:

A. $y = 144$
B. $y = \frac{11}{12}$
C. $y = 11$
D. $y = \frac{1}{11}$

Based on our solution, we can see that the correct answer is:

C. $y = 11$

Why is this the correct answer?

The correct answer is $y = 11$ because it is the solution to the equation $12y = 132$ . When we divide both sides of the equation by $12$ , we get $y = \frac{132}{12}$ , which simplifies to $y = 11$ . This is the only answer option that satisfies the original equation.

What about the other answer options?

Let's take a look at the other answer options:

A. $y = 144$ : This is not the correct answer because it does not satisfy the original equation. When we substitute $y = 144$ into the equation, we get $12(144) = 1728$ , which is not equal to $132$ .
B. $y = \frac{11}{12}$ : This is not the correct answer because it does not satisfy the original equation. When we substitute $y = \frac{11}{12}$ into the equation, we get $12(\frac{11}{12}) = 11$ , which is not equal to $132$ .
D. $y = \frac{1}{11}$ : This is not the correct answer because it does not satisfy the original equation. When we substitute $y = \frac{1}{11}$ into the equation, we get $12(\frac{1}{11}) = \frac{12}{11}$ , which is not equal to $132$ .

Conclusion

Q: What is a linear equation?

A: 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, where a, b, and c are constants, and 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. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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

A: The first step in solving a linear equation is to simplify the equation by combining like terms. This involves adding or subtracting the same value from both sides of the equation.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. In other words, a linear equation can be written in the form ax + b = c, while a quadratic equation can be written in the form ax^2 + bx + c = 0.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable(s) in the equation. If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.

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

A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by plugging the solution back into the original equation to make sure it's true.

Q: What if I have a linear equation with fractions?

A: If you have a linear equation with fractions, you can simplify the equation by multiplying both sides by the least common multiple (LCM) of the denominators. This will eliminate the fractions and make it easier to solve the equation.

Q: Can I solve a linear equation with variables on both sides?

A: Yes, you can solve a linear equation with variables on both sides. To do this, you need to add or subtract the same value from both sides of the equation to isolate the variable on one side.

Q: What if I have a linear equation with decimals?

A: If you have a linear equation with decimals, you can solve it just like any other linear equation. However, you may need to use a calculator to perform the calculations.

Q: Can I use algebraic methods to solve a linear equation?

A: Yes, you can use algebraic methods to solve a linear equation. These methods include factoring, the quadratic formula, and other techniques that can be used to solve linear equations.

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

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

Not simplifying the equation before solving it
Not checking the solution by plugging it back into the original equation
Not using the correct order of operations
Not simplifying fractions before solving the equation

Conclusion

In conclusion, solving linear equations is a straightforward process that involves isolating the variable and simplifying the equation. By following the steps outlined above, you can arrive at the correct solution to any linear equation. Remember to always check your work and make sure that the solution satisfies the original equation.