Solving Equations with Variables on Both Sides

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adapted from cdanstrom's presentation

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Solving Equations With Variables on Both Sides of the equal sign:

Solving Equations With Variables on Both Sides of the equal sign

Slide2:

Goal : Get the variable on one side of the equal (=) sign then solve. To do this we have to move the smaller variable. How do we move a variable? Apply the inverse operation to the whole term! EXAMPLE 3x + 2 = 4x - 1 -3x -3x 2 = x - 1 + 1 + 1 3 = x Important Notes Apply operations directly below like terms! Bring equal sign straight down

TRY THE FOLLOWING:

y = 1 TRY THE FOLLOWING 8y – 9 = -3y + 2 3 – 4x = 18 + x +3y +3y 11y – 9 = 2 +9 +9 11y = 11 11 11 +4x +4x 3 = 18 + 5x -18 -18 -15 = 5x 5 5 -3 = x

Multi-Step Example:

Multi-Step Example 3(x + 4) = 2(x - 1) 3x + 12 = 2x - 2 Distributive Property -2x -2x x + 12 = - 2 -12 -12 x = - 14 Then Solve!

Special Case #1 2x + 5 = 2x - 3:

Special Case #1 2x + 5 = 2x - 3 -2x -2x 5 = -3 But is this possible? NO!!! So the answer is NO SOLUTIONS

Slide6:

Special Case #2 3(x + 1) - 5 = 3x - 2 3x + 3 – 5 = 3x - 2 3x - 2 = 3x – 2 -3x -3x -2 = -2 This is always true! Infinitely many solutions

Your Favorite and Mine……:

Your Favorite and Mine…… WORD PROBLEMS Mr. Szabo needed to rent a moving van. Company A charges a rate of $90 per hour plus a $50 truck fee. Company B charges a $70 per hour plus fee plus a $90 truck fee. For what numbers of hours of rental is the cost for the two companies the same?

Slide8:

Define our variables first! Let h = the number of hours of rental Company A Company B $90 per hour plus $50 $70 per hour plus $90 = 90h + 50 = 70h + 90 -70h -70h 20h + 50 = 90 -50 -50 20h = 40 20 20 h = 2

Word Problem Answer:

Word Problem Answer The rental cost for the two companies is the same after 2 hours of rental. Hours Company A Company B h 90h + 50 70h + 90 0 $50 $90 1 $140 $160 2 $230 $230 3 $320 $300

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