Dave and Tom know the perimeter of a rectangle is \(24\) inches. The restrictions on the width of the rectangle are values between \(2\) and \(8\) inches. What are the lengths of the rectangle? Dave thinks that the easist way to determine the values for length of a rectangle is to substitute \(24\) for the perimeter, substitute values in for the width and solve for the length using the equation \(2l+2w=P\).
Tom thinks that it is easier to solve the equation for the length and then substitute \(24\) for the perimeter and values for the width to determine values for the length of the rectangle. Whom do you agree with and why? |
Solving Literal Equations
When you solve a literal equation, like writing an equation in function form, you need to isolate the variable you are solving for.
When you solve a literal equation, like writing an equation in function form, you need to isolate the variable you are solving for.
A quick note about equivalent equations.
These answers are both correct but look a little different: \( x= \frac{C}{A}-\frac{By}{A} \) and \( x= \frac{C-By}{A} \).
In the first equation \(C\) and \(By\) have been divided by \(A\) individually, rather than their difference being divided by \(A\). This is just an application of the distributive property. Remember that your answer may be correct but not look exactly like another answer.
These answers are both correct but look a little different: \( x= \frac{C}{A}-\frac{By}{A} \) and \( x= \frac{C-By}{A} \).
In the first equation \(C\) and \(By\) have been divided by \(A\) individually, rather than their difference being divided by \(A\). This is just an application of the distributive property. Remember that your answer may be correct but not look exactly like another answer.
Quick Check
a) Write the equation \(3x - 4y = -12\) in function form (so that \(y\) is a function of \(x\), solve for \(y\)).
b) Solve the equation for \(w\): \(P= 2l +2w \).
a) Write the equation \(3x - 4y = -12\) in function form (so that \(y\) is a function of \(x\), solve for \(y\)).
b) Solve the equation for \(w\): \(P= 2l +2w \).