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Solving 2 step equations 1. 2. 3. 4. Oppositeof what the equation says Do the _________ Do the ___________to Same steps both sides of = Use ______________ order of operations Backwards Justify your work! Mult. or Divide Add or Subtract BEFORE _________________ ________________ 3x + 8 = 23 -8 -8 sub prop = 3x = 15 3 3 div prop 2* = X = 5 mult id H - 4 = 7 2 +4 +4 add prop = H =11 *2 mult pr = 2 1H = 22 mult id H = 22 Jim buys 3 shirts and a pair of jeans for $50. The jeans cost $23. Write and equation to find the cost of each shirt. 3 s + J = 50 3 s + 23 = 50 -23 3s 3 -23 sub prop = = 27 3 div prop = s = 9 mult id Cost of each shirt is $9 Solving multi- step equations Like Terms by adding them together. 1. Combine __________ Variables on one side of the =. 2. Get all the ___________ Numbers on the OTHER side. 3. Get all the ___________ Change the Sign Cross the line and To finish solving, usually ___________ Divide 3x + 8 + 2x = 23 5x + 8 = 23 5x = 15 5 5 X=3 5T – 4 = 3T + 8 5T -3T -4 = 8 2T -4 = 8 2T = 8 +4 2T = 12 2 2 T=6 x Solve for x if the perimeter is 33 3x+4 3x+1 + 3x+4 + x = 33 3x+1 + 3x +4 + x = 33 7x + 5 = 33 7x = 33 - 5 7x = 28 7 7 X=4 3x+1 Solve for X 6x + 7 4x-9 6x + 7 = 4x - 9 6x – 4x + 7 = -9 2x + 7 = -9 -7 -7 2x = -16 X = -8 Solving Inequalities Symbols Rules Example Example Greater Than > Greater Than or equal > Less Than < Less Than or equal < Solve just like an equation, but check which way The inequality is going. MULTIPLYING OR DIVIDING BY A NEGATIVE (-) SWITCHES THE INEQUALITY! X+8 > 10 -8 -8 X>2 2x+7 < 3 -7 -7 2x < -4 2 2 x < -2 -4X – 1 < 11 0 1 2 3 4 -4 -3 -2 -1 0 1 -3 -2 -1 0 1 2 3 Solving Inequalities Greater Than > Less Than < Greater Than or equal Less Than or equal P7 > < Solve just like an equation, but check which way the inequality goes. MULTIPLYING OR DIVIDING BY A NEGATIVE (-) SWITCHES THE INEQUALITY! EX #1: X+8 > 10 X+8 > 10 -8 -8 X>2 EX #3: -4X – 1<11 -4X – 1 < 11 +1 +1 -4x < 12 -4 -4 0 1 2 3 4 ANY number greater than 2 makes this true! EX #2: 2X + 7 < 3 2x+7 < 3 -7 -7 2x < -4 2 2 x < -2 X > -3 SWITCH the sign!! -4 -3 -2 -1 0 1 ANY number less than or equal -2 makes this true! -3 -2 -1 0 1 2 3 Solving Literal Equations Literal Equation Solving Regular Equation An equation with more than 1 variable. Often a formula To SOLVE a literal equation, get one variable by itself. Show the regular solving steps, but DON’T DO THE MATH! 3 X + 5 = 14 -5 -5 Subtract the 5 : sub property 3x = 14-5 /3 / 3 Divide by 3 : division property X = (14-5)/3 = 9/3 = 3 Literal Equation 4X + 6Y = W -6Y -6Y Subtract the 6 : sub property 4x = W-6Y / 4 / 4 Divide by 4 : division property X = W-6Y 4 5 = (3N) 4 *4 *4 mult prop 20 = 3N /3 /3 div prop 20/3 = N A = (HB) Solve for B 2 *2 *2 mult prop 2A = H*B /H /H div prop 2A/H = B