1.3 Solving Equations with Variables on Both Sides

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1.3 Solving Equations with Variables on Both Sides

Example 1 Get all variables on the same side by using the addition/subtraction property of equality 2x – 2 = -3x + 3 +3x + 3x 5x – 2 = 3 + 2 + 2 5x = 5 5 5 x = 1

Example 2 6m + 5 -7m = 10 - 5m + 3 -m + 5 = -5m + 13 + 5m + 5m - 5 - 5 4m = 8 4 4 m = 2

You try! -2x = 3x + 10 -3x -3x -5x = 10 -5 -5 x = -2

Example 3

You Try!

Core Concept Special Solutions to Linear Equations - Identity: an equation that is true for all values of the variable. An Identity has infinitely many solutions.

You Try! 3(5x+2) = 15x -2(4y + 1) = -8y - 2

Distance upstream = Distance downstream Example 4 A boat leaves New Orleans and travels upstream on the Mississippi River for 4 hours. The return trip only takes 2.8 hours because the boat travels 3 miles per hour faster downstream because of the current. How far does the boat travel upstream? HINT: Distance = rate x time Distance upstream = Distance downstream

You try! Write and solve an equation to determine in how many months you would pay the same total amount for each internet service. Installation fee Price per month Company A $60.00 $42.95 Company B $25.00 $49.95