What is the solution to the linear equation?
[tex]d-10-2 d+7=8+d-10-3 d[/tex]
A. [tex]d=-5[/tex]
B. [tex]d=-1[/tex]
C. [tex]d=1[/tex]
D. [tex]d=5[/tex]
Answer (1)
Combine like terms on both sides of the equation: d − 10 − 2 d + 7 = 8 + d − 10 − 3 d becomes − d − 3 = − 2 d − 2 .
Add 2 d to both sides: d − 3 = − 2 .
Add 3 to both sides: d = 1 .
The solution to the linear equation is 1 .
Explanation
Analyze the problem We are given the equation d − 10 − 2 d + 7 = 8 + d − 10 − 3 d and asked to find the value of d that satisfies it. We will simplify both sides of the equation by combining like terms, and then isolate d to find its value.
Simplify both sides First, let's combine the terms with d and the constant terms on the left side of the equation: d − 2 d − 10 + 7 = − d − 3 Now, let's combine the terms with d and the constant terms on the right side of the equation: d − 3 d + 8 − 10 = − 2 d − 2 So the equation becomes: − d − 3 = − 2 d − 2
Isolate d Now, we want to isolate d . Add 2 d to both sides of the equation: − d + 2 d − 3 = − 2 d + 2 d − 2 d − 3 = − 2 Next, add 3 to both sides of the equation: d − 3 + 3 = − 2 + 3 d = 1
State the solution Therefore, the solution to the equation is d = 1 .
Examples
Linear equations are used in various real-life scenarios, such as calculating the cost of items, determining the distance traveled at a constant speed, or converting between different units of measurement. For example, if you know the hourly rate and the total earnings, you can use a linear equation to find the number of hours worked. Understanding how to solve linear equations is a fundamental skill in mathematics and has practical applications in everyday life.
