Solve for $y$.
$
\begin{array}{l}
y+4=3(x+5) \\
y=[?] x+\square
\end{array}
$
Answer (1)
Expand the right side of the equation: y + 4 = 3 x + 15 .
Isolate y by subtracting 4 from both sides: y = 3 x + 15 − 4 .
Simplify the equation: y = 3 x + 11 .
The solution is y = 3 x + 11 .
Explanation
Understanding the Problem We are given the equation y + 4 = 3 ( x + 5 ) and we want to solve for y and express it in the form y = [ ?] x + □ . This means we want to isolate y on one side of the equation and have the other side in the form of a linear expression m x + b , where m is the coefficient of x and b is a constant.
Expanding the Equation First, we need to expand the right side of the equation by distributing the 3 to both terms inside the parentheses:
y + 4 = 3 ( x + 5 )
y + 4 = 3 × x + 3 × 5
y + 4 = 3 x + 15
Isolating y Now, we want to isolate y on the left side of the equation. To do this, we subtract 4 from both sides of the equation:
y + 4 − 4 = 3 x + 15 − 4
y = 3 x + 11
Final Answer We have now solved for y and expressed it in the desired form y = m x + b . In this case, m = 3 and b = 11 . Therefore, the solution is y = 3 x + 11 .
Examples
Understanding linear equations like this is crucial in many real-world scenarios. For example, imagine you are running a small business and want to model your profits. If your profit y depends on the number of items you sell x , and you know that for each item you sell, your profit increases by $3, and you have a fixed cost of 11 ( p er ha p s d u e t o ini t ia l se t u p cos t s ) , t h e n t h ee q u a t i o n y = 3x + 11$ can represent your profit model. This allows you to predict your profit based on the number of items sold.
