Solving 2 step equations Opposite Do the _________ of what the equation says Do the ___________to both sides of = Use ______________ order of operations Justify your work! Same steps Backwards Add or Subtract Mult. or Divide ________________ BEFORE _________________ 3x + 8 = 23 H - 4 = 7 2 -8 -8 sub prop = +4 +4 add prop = 3x = 15 2* H =11 2 *2 mult pr = 3 3 div prop = X = 5 mult id 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 -23 sub prop = 3s = 27 3 3 div prop = s = 9 mult id Cost of each shirt is $9

Solving multi- step equations Combine __________ by adding them together. Get all the ___________ on one side of the =. Get all the ___________ on the OTHER side. Like Terms Variables Numbers Change the Sign Cross the line and To finish solving, usually ___________ Divide 3x + 8 + 2x = 23 5T – 4 = 3T + 8 5x + 8 = 23 5T -3T -4 = 8 2T -4 = 8 5x = 15 2T = 8 +4 5 5 2T = 12 X = 3 2 2 T = 6 3x+1 x Solve for x if the perimeter is 33 Solve for X 3x+4 6x + 7 4x-9 3x+1 + 3x+4 + x = 33 3x+1 + 3x +4 + x = 33 7x + 5 = 33 6x + 7 = 4x - 9 7x = 33 - 5 7x = 28 6x – 4x + 7 = -9 7 7 2x + 7 = -9 X = 4 -7 -7 2x = -16 X = -8

MULTIPLYING OR DIVIDING BY A NEGATIVE (-) SWITCHES THE INEQUALITY! Solving Inequalities > Greater Than Symbols Greater Than or equal > Less Than < Less Than or equal < Rules Solve just like an equation, but check which way The inequality is going. MULTIPLYING OR DIVIDING BY A NEGATIVE (-) SWITCHES THE INEQUALITY! Example X+8 > 10 0 1 2 3 4 -8 -8 X > 2 Example 2x+7 < 3 -4 -3 -2 -1 0 1 -7 -7 2x < -4 2 2 x < -2 -4X – 1 < 11 -3 -2 -1 0 1 2 3

MULTIPLYING OR DIVIDING BY A NEGATIVE (-) SWITCHES THE INEQUALITY! Solving Inequalities P 7 Greater Than > Greater Than or equal > Less Than or equal < Less Than < 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 ANY number greater than 2 makes this true! 0 1 2 3 4 X+8 > 10 -8 -8 EX #2: 2X + 7 < 3 X > 2 2x+7 < 3 -7 -7 -4 -3 -2 -1 0 1 2x < -4 2 2 ANY number less than or equal -2 makes this true! EX #3: -4X – 1<11 x < -2 -4X – 1 < 11 +1 +1 -4x < 12 -3 -2 -1 0 1 2 3 -4 -4 X > -3 SWITCH the sign!!

Solving Literal Equations An equation with more than 1 variable. Often a formula Solving To SOLVE a literal equation, get one variable by itself. Show the regular solving steps, but DON’T DO THE MATH! Regular Equation 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 A = (HB) 2 Solve for B *4 *4 *2 *2 mult prop mult prop 20 = 3N 2A = H*B /3 /3 div prop /H /H div prop 20/3 = N 2A/H = B