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Chapter 8: Problem 102

In the following exercises, solve the equation. $$0.25 d+0.10 d=6-0.75$$

Short Answer

Expert verified
d = 15

Step by step solution

01

Combine like terms

You have the equation: 0.25d + 0.10d = 6 - 0.75 Combine the terms with the variable on the left side of the equation. 0.25d + 0.10d = 0.35d
02

Simplify the constants on the right-hand side

Simplify the right side of the equation by subtracting: 6 - 0.75 = 5.25 Now the equation looks like: 0.35d = 5.25
03

Solve for the variable

To isolate the variable, divide both sides of the equation by 0.35: 0.35d / 0.35 = 5.25 / 0.35 This results in: d = 15

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combining like terms
Combining like terms is the first step when simplifying many algebraic equations. Like terms are terms that contain the same variable raised to the same power. For instance, in the equation given, 0.25d and 0.10d are like terms because they both have the variable d.
To combine them, simply add their coefficients: 0.25 + 0.10 = 0.35. Therefore, 0.25d + 0.10d becomes 0.35d.
This step is essential for simplifying the equation and making it easier to solve. Combining like terms reduces the complexity of the equation, helping you to focus on the core arithmetic operations needed to find the variable.
Simplifying equations
Once we have combined like terms, the next step is to simplify other parts of the equation wherever possible. Simplifying equations makes them less complex and easier to solve.
Looking at our exercise, the equation after combining like terms is: 0.35d = 6 - 0.75.
Simplify the right-hand side by performing the subtraction: 6 - 0.75 = 5.25.
Simplifying constants and other arithmetic operations on one side of the equation leads to a cleaner and more straightforward equation. In this case, the simplified equation is now: 0.35d = 5.25.
This process is crucial as it prepares the equation for the final steps needed to isolate the variable.
Isolating variables
The final step in solving the equation is to isolate the variable. Isolating the variable means getting the variable alone on one side of the equation.
In our simplified equation 0.35d = 5.25, we need to isolate d. To do this, we divide both sides of the equation by the coefficient of d, which is 0.35.
Perform the division: \(\frac{0.35d}{0.35} = \frac{5.25}{0.35}\).
This calculation simplifies to d = 15.
By isolating the variable, we solve the equation, finding the value of d. This final step transforms an algebraic expression into a simple numerical value, providing the solution to the problem.

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