b. $3 x+2-4 x=7 x-2$
Answer (2)
The solution to the equation 3 x + 2 − 4 x = 7 x − 2 is x = 2 1 . The steps involved combining like terms, isolating x terms, and solving for x . This process showed us how to manipulate the equation to find the value of x .
;
Combine like terms: − x + 2 = 7 x − 2 .
Add x to both sides: 2 = 8 x − 2 .
Add 2 to both sides: 4 = 8 x .
Divide by 8: x = 2 1 .
Explanation
Understanding the Problem We are given the equation 3 x + 2 − 4 x = 7 x − 2 . Our goal is to solve for x . We will achieve this by simplifying the equation and isolating x on one side.
Combining Like Terms First, we combine like terms on the left side of the equation: 3 x − 4 x = − x . So the equation becomes − x + 2 = 7 x − 2 .
Isolating x Terms Next, we want to isolate the x terms. We can add x to both sides of the equation to get 2 = 7 x + x − 2 , which simplifies to 2 = 8 x − 2 .
Isolating Constant Terms Now, we isolate the constant terms by adding 2 to both sides of the equation: 2 + 2 = 8 x , which simplifies to 4 = 8 x .
Solving for x Finally, we solve for x by dividing both sides of the equation by 8: x = 8 4 . Simplifying the fraction, we get x = 2 1 .
Examples
Linear equations are used in everyday life to calculate costs, distances, and proportions. For example, if you want to determine how many hours you need to work to earn a specific amount of money, you can set up a linear equation. Similarly, if you are planning a road trip and want to calculate the time it will take to reach your destination, you can use a linear equation to model the relationship between distance, speed, and time. Understanding how to solve linear equations is a fundamental skill that has numerous practical applications.
