3.4 Solving Equations with Variables on Both Sides, p129 Warm up

1. 3.4 Solving Equations with Variables on Both Sides, p129 Warm up Name the property. 2. │14-24│-│- 3 - 7│= 1. 3. 4. AF4.1 Solve 2-step linear equations… interpret the solutions… & verify the reasonableness of the results. Also: AF1.1 LO:I will interpret equations with variables on both sides using simplifying, collecting of the variable terms on one side, & finally- isolating the variable. Helpful Hint

2. Real Life Applications 1. The square and the triangle have equivalent perimeters. Formulate and interpret an algebraic equation to find the perimeter of the triangle. Write an expression describe the perimeter of the square. Write an expression to describe the perimeter of the triangle. 2. Mom leaves home driving at a steady speed of 50 mph. Dad leaves home one hour later, following Mom’s route. He drives at a steady rate of 60 mi/h. How long after Mom leaves will Dad catch up? Distance Mom travels = Distance Dad travels If m = Mom’s time, then (m – 1) = Dad’s time minus 1 hour 50m =60(m - 1 ) Use the ___________________ Property. Simplify. Collect the variable terms on one side. Undo to ________________ the variable. When?

3. 1st simplify by combining like terms or clearing fractions. • 2nd add or subtract to collect variable terms on one side of the equation. • Finally, use properties of equality to isolate the variable. 3. 10z – 15 – 4z = 8 – 2z – 15 4. Florist A sells a rose bouquet for $40 plus $3 for every rose. Florist B sells a similar bouquet for $26 plus $5 for every rose. Find the number of roses that would make both florists' bouquets cost the same price. What is the price? Florist A = Florist B If $40 + $3r is Florist A’s cost, then ____________________ is Florist B’s cost Simplify. Collect the variable terms on one side. Undo to ________________ the variable. The two bouquets from either florist would cost the same when purchasing ___ roses. NOTE: To find the cost for a bouquet with ___ roses at either florist substitute ___ for r.

4. 20 1 20 1 7 10 7 10 3y 5 3y 5 y 5 y 5 3 4 3 4 5. + – = y – 1st Clear the fractions , Multiply by the LCD ___. Use __________________ Property. Simplify. Combine ______________. Collect the ______ terms on one side. Undo to _____________ the variable. ( ) ( ) + – = y – 4y +12y – 15= 20y –14 __y – 15 = __y – 14 6. 1st Clear the fractions , Multiply by the LCD ___. Use Distributive Property to kiss those __________ away. Simplify, collect, isolate.

5. Remember: When variables in an equation are eliminated, & the resulting statement is false, the equation has no solution. Your solution using substitution. • 1st simplify by combining like terms or clearing fractions. • 2nd add or subtract to collect variable terms on one side of the equation. • Finally, use properties of equality to isolate the variable. 1. 4x + 6 = x 2. 9b – 6 = 5b + 18 3. 12z – 12 – 4z = 6 – 2z + 32

6. Remember: When variables in an equation are eliminated, & the resulting statement is false, the equation has no solution. Your solution using substitution. 5. 9w + 3 = 9w + 7 3 ≠ 7 NO SOLUTION

7. Remember: When variables in an equation are eliminated, & the resulting statement is false, the equation has no solution. Your solution using substitution. 3. 2(3x + 11) = 6x + 4 8. 3b – 2 = 2b + 12 9. 3w + 1 = 3w + 8 10. 12z – 12 – 4z = 6 – 2z + 32

8. 11. Marla’s Gift Baskets sells a muffin basket for $22.00 plus $2.25 for every hot chocolate. A competing service sells a similar muffin basket for $16.00 plus $3.00 for every hot chocolate. Find the number of hot chocolates that would make both baskets cost the same price. 12. An apple has about 30 calories more than an orange. Five oranges have about as many calories as 3 apples. How many calories are in each? An orange has ___ calories. An apple has ___ calories. HW- 3.4 RM & 3.4 SR p133 even