Solving Equations with Variables on both sides

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Presentation transcript:

Solving Equations with Variables on both sides Objectives: To solve equations with variables on both sides of the equal sign.

STEPS TO SOLVING LINEAR EQUATIONS DON’T CALL ME AFTER MIDNIGHT Distribute Combine like terms Move the variables to one side Add/subtract Multiply/divide DCMAM IS A ROAD MAP BUT NOT THE ONLY WAY TO SOLVE AN EQUAITON

Which of the following could be the first step? 4x + 27 = 3x A) Subtract 4x from both sides B) Subtract 3x from both sides C) Subtract 27 from both sides D) Combine like terms (4x and 3x) to get 7x

Example 1 Solve. 4x + 27 = 3x -4x -4x 27 = -1x -1 -1 -27 = x Move variable to one side -4x -4x 27 = -1x Divide on both sides -1 -1 -27 = x

How else can we solve example 1? 4x + 27 = 3x Move variable to one side -3x -3x x + 27 = 0 Subtract on both sides -27 -27 x = - 27

How else can we solve example 1? 4x + 27 = 3x -27 -27 Subtract on both sides 4x = 3x - 27 Move variable to one side -3x -3x x = - 27

Which of the following could be the first step? 3(4 + 4x) = 12x + 12 A) Subtract 12x from both sides B) Divide each term by 3 C) Distribute D) Combine (4 and 4x) and (12x and 12)

Example 2 Solve. 3(4 + 4x) = 12x + 12 12 + 12x = 12x +12 -12x -12x distribute 12 + 12x = 12x +12 notice anything? -12x -12x Move variable to one side 12 = 12 ALL REAL NUMBERS Variables cancel out End with same number on both sides of = Means that if you plug in any number into the equation it will work. What does this answer mean? NO SOLUTION Variables cancel out End with different number on both sides of = Means that there is no number that will work in the equation.

How else can we solve example 2? Divide each term by 3 Move variable to one side What does this answer mean? ALL REAL NUMBERS

Which of the following could be the first step? A) Multiply each term by 4/3 B) Multiply each term by 4 C) Distribute D) Combine (4 and 3x) and (12 and 8x)

Example 3 distribute Move variable to the one side Subtract to both sides Divide to both sides

How else can we solve Example 3? (Watch) Multiply all terms by 4 Divide 3 to both sides Distribute Move variable to one side Subtract on both sides Divide both sides by 4

Summary How would you clear the fractions in the following problem? How do you know whether to move the variables to the left side of the equal sign or the right side?