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

Clare solves an equation, but when she checks her answer she notices that her solution is incorrect. She knows she made a error, but she can’t find it. Help Clare find the error and correctly solve 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.

Kiran wrote the expression \(x-10\) to represent this number puzzle: “Pick a number, add -2, and multiply by 5.”

Lin thinks Kiran made a mistake.

1. How can she convince Kiran he made a mistake?
2. What would be a correct expression for this number puzzle?

Label the arrows to describe each move.

Represent the solution for each inequality on the number line.

1. \(x>7\)

   

2. \(x\geq\text-4.2\)