Solve for $y: 2 y-3 y+5 y+10=42$
A. $y=13$
B. $y=8$
C. $y=-8$
D. $y=128$
Answer (1)
Combine like terms: 2 y − 3 y + 5 y = 4 y .
Subtract 10 from both sides: 4 y = 42 − 10 = 32 .
Divide both sides by 4: y = 4 32 = 8 .
The solution is 8 .
Explanation
Understanding the Problem We are given the equation 2 y − 3 y + 5 y + 10 = 42 and asked to solve for y . This is a linear equation, and our goal is to isolate y on one side of the equation.
Combining Like Terms First, we combine the terms with y on the left side of the equation: 2 y − 3 y + 5 y = ( 2 − 3 + 5 ) y = 4 y So the equation becomes: 4 y + 10 = 42
Isolating the Variable Term Next, we subtract 10 from both sides of the equation to isolate the term with y :
4 y + 10 − 10 = 42 − 10 4 y = 32
Solving for y Finally, we divide both sides of the equation by 4 to solve for y :
4 4 y = 4 32 y = 8
Final Answer Therefore, the solution to the equation is y = 8 .
Examples
Linear equations like this one are used in many real-world situations. For example, if you are saving money and want to know how many weeks it will take to reach a certain goal, you can set up a linear equation to model your savings. If you save a fixed amount each week and start with some initial savings, the equation can help you determine when you'll have enough money. Understanding how to solve these equations is a fundamental skill in personal finance and many other areas.
