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Learning Targets

• I can use the idea of doing the same to each side to solve equations that have negative numbers or solutions.

When we want to find a solution to an equation, sometimes we just think about what value in place of the variable would make the equation true. Sometimes we perform the same operation on each side (for example, subtract the same amount from each side). The balanced hangers helped us to understand that doing the same to each side of an equation keeps the equation true.

Since negative numbers are just numbers, then doing the same thing to each side of an equation works for negative numbers as well. Here are some examples of equations that have negative numbers and steps you could take to solve them.

Doing the same thing to each side maintains equality even if it is not helpful to solving for the unknown amount. For example, we could take the equation -3x + 7 = -8 and add -2 to each side:

If -3x + 7 = -8 is true then -3x + 5 = 10 is also true, but we are no closer to a solution than we were before adding -2. We can use moves that maintain equality to make new equations that all have the same solution. Helpful combinations of moves will eventually lead to an equation like x = 5, which gives the solution to the original equation (and every equation we wrote in the process of solving).

Solve each equation. Be prepared to explain your reasoning.