Matching the Values to the Options

Oct 13, 2025 by recoveryshake.com 130 views

In mathematics, solving equations is a crucial skill that helps us find the value of a variable. An equation is a statement that says two things are equal, and it can be solved by isolating the variable on one side of the equation. In this article, we will solve five different equations and match the value of the variable to the given options.

Solving the First Equation: $3p = 72$

To solve the equation $3p = 72$ , we need to isolate the variable $p$ . We can do this by dividing both sides of the equation by 3.

Step 1: Divide both sides of the equation by 3.

\frac{3p}{3} = \frac{72}{3}

Step 2: Simplify the equation.

p = 24

Therefore, the value of the variable $p$ is 24.

Solving the Second Equation: $2x = 4$

To solve the equation $2x = 4$ , we need to isolate the variable $x$ . We can do this by dividing both sides of the equation by 2.

Step 1: Divide both sides of the equation by 2.

\frac{2x}{2} = \frac{4}{2}

Step 2: Simplify the equation.

x = 2

Therefore, the value of the variable $x$ is 2.

Solving the Third Equation: $12 = \frac{h}{6}$

To solve the equation $12 = \frac{h}{6}$ , we need to isolate the variable $h$ . We can do this by multiplying both sides of the equation by 6.

Step 1: Multiply both sides of the equation by 6.

12 \times 6 = \frac{h}{6} \times 6

Step 2: Simplify the equation.

72 = h

Therefore, the value of the variable $h$ is 72.

Solving the Fourth Equation: $81 = \frac{r}{9}$

To solve the equation $81 = \frac{r}{9}$ , we need to isolate the variable $r$ . We can do this by multiplying both sides of the equation by 9.

Step 1: Multiply both sides of the equation by 9.

81 \times 9 = \frac{r}{9} \times 9

Step 2: Simplify the equation.

729 = r

Therefore, the value of the variable $r$ is 729.

Solving the Fifth Equation: $\frac{n}{3} = 21$

To solve the equation $\frac{n}{3} = 21$ , we need to isolate the variable $n$ . We can do this by multiplying both sides of the equation by 3.

Step 1: Multiply both sides of the equation by 3.

\frac{n}{3} \times 3 = 21 \times 3

Step 2: Simplify the equation.

n = 63

Therefore, the value of the variable $n$ is 63.

Matching the Values to the Options

Now that we have solved the five equations, we can match the value of the variable to the given options.

The value of the variable $p$ is 24, which matches option a.
The value of the variable $x$ is 2, which does not match any of the options.
The value of the variable $h$ is 72, which does not match any of the options.
The value of the variable $r$ is 729, which matches option d.
The value of the variable $n$ is 63, which matches option e.

Therefore, the correct matches are:

$p = 24$ (option a)
$r = 729$ (option d)
$n = 63$ (option e)

In our previous article, we solved five different equations and matched the value of the variable to the given options. In this article, we will answer some frequently asked questions (FAQs) related to solving equations and matching values.

Q: What is an equation?

A: An equation is a statement that says two things are equal. It can be written in the form of $a = b$ , where $a$ and $b$ are expressions or values.

Q: How do I solve an equation?

A: To solve an 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 order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I match the value of the variable to the given options?

A: To match the value of the variable to the given options, you need to compare the value of the variable to each option and choose the one that matches.

Q: What if I get stuck while solving an equation?

A: If you get stuck while solving an equation, try the following:

Read the equation carefully and make sure you understand what it's asking for.
Try to isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Use the order of operations to evaluate any expressions inside parentheses, exponents, multiplication and division, and addition and subtraction.
If you're still stuck, try drawing a diagram or using a different method to solve the equation.

Q: Can I use a calculator to solve equations?

A: Yes, you can use a calculator to solve equations. However, make sure you understand the steps involved in solving the equation and can explain the solution in your own words.

Q: How do I check my answer?

A: To check your answer, plug the value of the variable back into the original equation and make sure it's true. If the equation is true, then your answer is correct.

Q: What if I make a mistake while solving an equation?

A: If you make a mistake while solving an equation, don't worry! Just go back and recheck your work. Make sure you understand the steps involved in solving the equation and can explain the solution in your own words.

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

A: Yes, you can use a graphing calculator to solve equations. Graphing calculators can help you visualize the solution to an equation and can be a useful tool for solving equations.

Q: How do I use a graphing calculator to solve equations?

A: To use a graphing calculator to solve equations, follow these steps:

Enter the equation into the calculator.
Use the calculator to graph the equation.
Use the calculator to find the solution to the equation.
Check your answer by plugging the value of the variable back into the original equation.

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

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

Not following the order of operations.
Not isolating the variable on one side of the equation.
Not checking your answer.
Not using a calculator to check your answer.

By following these tips and avoiding common mistakes, you can become a master of solving equations and matching values!