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Solve Equations With Variables on Both Sides Section 1.5 Advanced Algebra 1 Steps to Solve Equations with Variables on Both Sides 1) Simplify each side Get rid of double Negatives Get rid of fractions Distribute Combine Like Terms 2) Move variables to same side “Smaller to the bigger” 3) Solve by using INVERSE Operations bkevil Use Steps to Solve Equation: -3x + 4 = 5x – 8 +3x +3x 4 = 8x - 8 +8 +8 12 = 8x 8 8 x = 3/2 Get variables on same side of equation – use inverse operation (add 3x) Solve 2 step equation Use Steps to Solve Equation: 2(x + 7) + 3 = 5x - 1 2x + 14 + 3 = 5x – 1 2x + 17 = 5x - 1 -2x -2x 17 = 3x - 1 +1 +1 18 = 3x 3 3 x= 6 distribute Combine like terms Get variables on same side – use inverse operation Solve 2 step equation Use Steps to Solve Equation: 4(1 – 2x) = 4 – 6x 4 – 8x = 4 - 6x +8x + 8x 4 = 4 + 2x -4 -4 0 = 2x 2 2 x= 0 Get rid of ( ) -- distribute Get variables on same side – use inverse operation (add 8x) Solve 2 step equation Use Steps to Solve Equation: 9 + 5x = 5x + 9 -5x -5x 9=9 Infinite Solutions Get variables on same side of equation – use inverse operation (subtract 5x) When solving, if you get a TRUE STATEMENT, then that means that any real number works. Use Steps to Solve Equation: 6x – 1 = 6x – 8 -6x -6x -1 = - 8 x = no solutions The solution is no real numbers or empty set Get variables on same side of equation – use inverse operation (subtract 6x) The variables zeroed out and remaining is a false statement where a number is equal to a different number, so there will be no number that will work in the equation. 3 1 1 3 x = x 5) Solve 8 4 2 4 1. 2. 3. 4. 5. 6. 7. 8. 9. Clear the fraction – multiply each term by the LCD Simplify Add 2x to both sides Simplify Add 6 to both sides Simplify Divide both sides by 6 Simplify Check your answer 3 1 1 3 (8) - (8) x = (8) x - (8) 8 4 2 4 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 +6 +6 9 = 6x 6 6 3 or 1.5 = x 2 3 1 1 3 1.5 1.5 8 4 2 4 Solve the equation. Check your answer. 0.5 + 0.3y = 0.7y – 0.3 0.5 + 0.3y = 0.7y – 0.3 –0.3y –0.3y 0.5 = 0.4y – 0.3 +0.3 + 0.3 0.8 = 0.4y 2=y 1: Move variable to one side 2: add/subtract 3: Multiple/divide Simplifying Each Side Before Solving Equations 4 – 6a + 4a = –1 – 5(7 – 2a) D: Distributive P. 4 – 6a + 4a = –1 –5(7 – 2a) 4 – 6a + 4a = –1 –5(7) –5(–2a) 4 – 6a + 4a = –1 – 35 + 10a 4 – 2a = –36 + 10a +2a +2a 4 = -36 + 12a C: Combine like terms M: move variable to One side 4 + 36 40 = -36 + 12a A: add/subtract +36 = 12a M: multiply/divide Solve the equation. Check your answer. D: Distributive Property M: Move variable to one side 3=b–1 +1 4=b +1 A: Add/subtract Solve the equation. 1. 2m – 6 + 4m = 12 ANSWER 3 2. 6a – 5(a – 1) = 11 ANSWER 6 Create an equation, then solve the equation. 3. A charter bus company charges $11.25 per ticket plus a handling charge of $.50 per ticket, and a $15 fee for booking the bus. If a group pays $297 to charter a bus, how many tickets did they buy? ANSWER 24 tickets Solve the equation. 1. 8g – 2 + g = 16 ANSWER 2. 2 3b + 2(b – 4) = 47 ANSWER 11 3. –6 + 4(2c + 1) = –34 ANSWER –4 4. 2 (x – 6) = 12 3 ANSWER 24 5. Joe drove 405 miles in 7 hours. He drove at a rate of 55 miles per hour during the first part of the trip and 60 miles per hour during the second part. How many hours did he drive at a rate of 55 miles per hour? ANSWER 3h