1.) Consecutive integers are integers that follow each other in order (for example 5, 6, 7). Find three consecutive integers whose sum is ) You have a 90-pound calf you are raising for a 4-H project. You expect the calf to gain 65 pounds per month. In how many months will the animal weigh 1000 pounds? 3.) In any triangle, the sum of the measures of the angles is 180°. In triangle ABC, ﮮ A is four times as large as ﮮ B. Angle C measures 20° less than ﮮ B. Find the measure of each angle.
1.) Consecutive integers are integers that follow each other in order (for example 5, 6, 7). Find three consecutive integers whose sum is 84.
2.) You have a 90-pound calf you are raising for a 4-H project. You expect the calf to gain 65 pounds per month. In how many months will the animal weigh 1000 pounds?
3.) In any triangle, the sum of the measures of the angles is 180°. In triangle ABC, ﮮ A is four times as large as ﮮ B. Angle C measures 20° less than ﮮ B. Find the measure of each angle.
Solving Equations with Variables on Both Sides
Steps 1.) Circle all terms with the variable 2.) Decide if the variables are on the same side of the equal sign. If on the same side of the equal sign, combine like terms. If on different sides… 3.) Decide which term is smaller. 4.) Move the smaller term to the other side by dropping it down and changing the sign. 5.) Solve as before.
Examples 1.) 3x + 5 = 5x + 7
Examples 2.) 3x + 4 = -2x + 14
Examples 3.) 3x + 5 = 2x – 6
Try 1.) 4x – 8 = -2x + 10
Try 2.) 10x + 12 = 12x – 4
Solving Equations True and False Statements
Sometimes when you solve equations, your variable disappears. When this happens, your result is either a true statement or a false statement. If true, the answer is “all reals,” meaning you can plug any number in and get a true statement. If false, the answer is no solution, meaning there is no value that will give you a true statement.
Examples: Solve: 1.) 2x + 5 = 2x – 3 2.) 2(x+5) = 2x + 10
Examples: 3.) 3(x – 4) – 3x = 12
Try: 1.) x + 5 = x ) 3(x + 2) = 3x ) 5(x – 3) = 5x + 15