What is the solution to the linear equation?
$2.8 y+6+0.2 y=5 y-14$
A. $y=-10$
B. $y=-1$
C. $y=1$
D. $y=10$
Answer (1)
Combine like terms on the left side: 2.8 y + 0.2 y + 6 = 3 y + 6 .
Rewrite the equation: 3 y + 6 = 5 y − 14 .
Isolate y terms and constant terms: 2 y = 20 .
Solve for y : y = 10 . The solution to the linear equation is 10 .
Explanation
Understanding the equation We are given the equation 2.8 y + 6 + 0.2 y = 5 y − 14 and asked to find the value of y that satisfies it. We will solve it step by step by combining like terms and isolating y .
Combining like terms First, let's combine the terms with y on the left side of the equation: 2.8 y + 0.2 y = 3 y . So the equation becomes 3 y + 6 = 5 y − 14 .
Isolating y terms Next, we want to isolate the y terms on one side and the constant terms on the other side. Let's subtract 3 y from both sides of the equation: 3 y + 6 − 3 y = 5 y − 14 − 3 y , which simplifies to 6 = 2 y − 14 .
Isolating constant terms Now, let's add 14 to both sides of the equation: 6 + 14 = 2 y − 14 + 14 , which simplifies to 20 = 2 y .
Solving for y Finally, let's divide both sides of the equation by 2 to solve for y : 2 20 = 2 2 y , which simplifies to y = 10 .
Final Answer Therefore, the solution to the equation is y = 10 .
Examples
Linear equations are used in everyday life to calculate costs, distances, and other quantities. For example, if you know the cost of each item and the total cost, you can use a linear equation to find the number of items you bought. Suppose you bought several apples for $0.75 each and a banana for $0.50, and the total cost was $5.00. The equation would be 0.75 x + 0.50 = 5.00 , where x is the number of apples. Solving for x would tell you how many apples you purchased.
