Solve for $y$.
$
\begin{array}{l}
y-4=2(x+5) \\
y=[?] x+\square
\end{array}
$
Answer (1)
Expand the right side of the equation: y − 4 = 2 x + 10 .
Isolate y by adding 4 to both sides: y = 2 x + 10 + 4 .
Simplify the equation: y = 2 x + 14 .
The solution is y = 2 x + 14 .
Explanation
Understanding the Problem We are given the equation y − 4 = 2 ( 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 expand the right side of the equation by distributing the 2 to both terms inside the parentheses:
y − 4 = 2 ( x + 5 )
y − 4 = 2 x + 2 ( 5 )
y − 4 = 2 x + 10
Isolating y Next, we isolate y by adding 4 to both sides of the equation:
y − 4 + 4 = 2 x + 10 + 4
y = 2 x + 14
Final Answer Therefore, the equation is now in the form y = 2 x + 14 . The coefficient of x is 2 and the constant term is 14 .
Examples
Understanding linear equations is crucial in many real-world scenarios. For instance, imagine you're saving money. If you start with $4 and save $2 every week, the equation y = 2x + 4 models your total savings (y) after x weeks. This equation helps you predict how much money you'll have saved after a certain period, which is a practical application of solving for y in a linear equation.
