Lesson 5

Solve each of these equations. Explain or show your reasoning.

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Clare’s mistake and what is the solution to the equation?

\(\begin{align} 12(5+2y)&=4y-(5-9y)\\ 72+24y&=4y-5-9y\\ 72+24y&=\text-5y-5\\ 24y&=\text-5y-77\\ 29y&=\text-77\\ y&=\frac {\text{-}77}{29}\ \end{align}\)

Solve each equation, and check your solution.

One solution of the equation is \((3,2)\).

One solution of the equation is \((\text-1,1)\).

One solution of the equation is \(\left(1,\frac32\right)\).

There are 2 solutions.

There are infinitely many solutions.

The equation of the line is \(y=\frac14 x +\frac54\).

The equation of the line is \(y=\frac54 x +\frac14\).

A participant in a 21-mile walkathon walks at a steady rate of 3 miles per hour. He thinks, “The relationship between the number of miles left to walk and the number of hours I already walked can be represented by a line with slope \(\text-3\).” Do you agree with his claim? Explain your reasoning.