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# Two Step Equations with Decimals

Equations serve as the key to unlocking mathematical mysteries, and in this article, we embark on an exciting journey into the realm of two-step equations with decimals, tailored specifically for Grade 7 students.

Solving two-step equations with decimals is an important skill for Grade 7 students to develop. These equations involve two operations and incorporate decimal numbers, adding an extra layer of complexity to the problem-solving process.

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Clearing the Decimals:

The first step in solving two-step equations with decimals is to eliminate the decimal points. This can be achieved by multiplying both sides of the equation by a power of 10 that will shift the decimal places to the right. By doing so, the decimals are converted to whole numbers, simplifying the equation. Isolating the Variable:

Once the decimals are cleared, the goal is to isolate the variable on one side of the equation. This involves applying inverse operations, such as addition or subtraction, and multiplication or division, to both sides of the equation. The objective is to perform the necessary steps to isolate the variable and obtain its value.

Checking the Solution:

After finding a solution for the variable, it is crucial to check the validity of the solution by substituting it back into the original equation. By evaluating both sides of the equation and ensuring they are equal, you can verify the accuracy of the solution. Checking the solution reinforces the understanding of the equation and ensures the correct value for the variable.

By following these steps and applying the principles of algebra, Grade 7 students can confidently solve two-step equations with decimals. It is important to pay attention to the decimal places and perform operations accurately throughout the solution process.

## Solved Examples

Formula 1: Clearing the Decimals
To clear the decimals in an equation, multiply both sides of the equation by a power of 10 that will shift the decimal places to the right.

Example:
Solve the equation: 0.5x + 1.2 = 3.1

Step 1: Clearing the Decimals
Since there are two decimal numbers involved, we can multiply both sides of the equation by 10 to eliminate the decimals:

10 * (0.5x + 1.2) = 10 * 3.1
5x + 12 = 31

Formula 2: Isolating the Variable
To isolate the variable in a two-step equation, apply inverse operations to both sides of the equation.

Example:
Using the equation from the previous example: 5x + 12 = 31

Step 2: Isolating the Variable
To isolate the variable term, subtract 12 from both sides of the equation:

5x + 12 – 12 = 31 – 12
5x = 19
Next, divide both sides of the equation by the coefficient of x (which is 5) to solve for x:

(5x)/5 = 19/5
x = 3.8

So, the solution to the equation is x = 3.8.

Formula 3: Checking the Solution
After obtaining a value for the variable, it is important to check the solution’s validity by substituting it back into the original equation.

Example:
Using the original equation: 0.5x + 1.2 = 3.1

Step 3: Checking the Solution
Substitute the value x = 3.8 back into the original equation:

0.5(3.8) + 1.2 = 3.1
1.9 + 1.2 = 3.1
3.1 = 3.1

Since both sides of the equation are equal, the solution x = 3.8 is valid.

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## Real-life Examples

Shopping and Sales:
When shopping, calculating discounts and final prices often involves solving equations with decimals. For instance, determining the discounted price of an item during a sale or applying a percentage off requires solving a two-step equation with decimals.

Financial Management:
Managing personal finances requires solving equations with decimals. For example, determining monthly expenses, budgeting, calculating interest rates, or finding mortgage payments involve solving two-step equations with decimals.

Recipe Scaling:
Scaling recipes to adjust serving sizes often requires solving equations with decimals. If a recipe is designed to serve four people but needs to be adjusted to serve six, solving a two-step equation with decimals can determine the new ingredient quantities accurately.

Measurement Conversions:
Converting measurements between different units may involve solving equations with decimals. For instance, converting between metric and imperial units or converting time between hours, minutes, and seconds can require solving two-step equations with decimals.

Engineering and Construction:
Engineers and construction professionals often encounter equations with decimals in their work. Calculating dimensions, quantities, or adjusting designs may involve solving two-step equations with decimals to ensure accuracy in measurements and constructions.

Science Experiments:
In scientific experiments, analyzing data and interpreting results may require solving equations with decimals. For instance, calculating concentrations, dilutions, or converting units of measurement in scientific observations or experiments can involve two-step equations with decimals.

## FAQs

##### What are two-step equations with decimals?

Two-step equations with decimals are algebraic equations that involve two operations and include decimal numbers. These equations require multiple steps to isolate the variable and find its value. They often involve addition, subtraction, multiplication, or division, combined with decimal numbers. Solving two-step equations with decimals requires applying inverse operations to simplify the equation and isolate the variable.

##### How do I solve two-step equations with decimals?

To solve a two-step equation with decimals, follow these steps:

Clear the decimals by multiplying both sides of the equation by a power of 10 that will shift the decimal places.
Simplify the equation by performing the necessary operations to isolate the variable term on one side.
Solve for the variable by applying inverse operations, such as addition or subtraction, multiplication or division, to both sides of the equation.
Check the solution by substituting the found value back into the original equation and ensuring both sides are equal.

##### How can I work with decimals in two-step equations?

When working with decimals in two-step equations, it is important to pay attention to decimal places and perform operations accurately. Keep track of the number of decimal places in the equation and align the decimal points in calculations to maintain accuracy. Be mindful of carrying decimals throughout the solution process and maintain consistent decimal precision in the final answer.

##### Can I check my solution in two-step equations with decimals?

Yes, it is crucial to check the solution in two-step equations with decimals. After finding the value for the variable, substitute it back into the original equation and evaluate both sides. If both sides are equal, the solution is valid. Checking the solution helps ensure accuracy and confirms that the equation has been solved correctly.

##### Why are two-step equations with decimals important?

Two-step equations with decimals are important as they enhance problem-solving skills, reinforce algebraic concepts, and provide real-world applications. Mastering these equations helps students develop critical thinking, logical reasoning, and numerical fluency. Understanding how to solve two-step equations with decimals prepares Grade 7 students for more advanced mathematical concepts and equips them with valuable skills applicable in various fields and everyday life situations. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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