2 Multi-Step Inequalities 4x-8>6x+4 Step 1:

Put all variables on one side 4x-8>6x+4 -4x -4x -8>2x+4 Step 1 Step 2 Step 3 Step 2: Isolate the Variable -8>2x+4 -4 -4 -12>2x Step 3: Solve -12>2x 2 -6>x

or

x<-6 l x<-6 Final Answer l How to solve 2 3 Put all variables on 1 side Isolate the variable Solve normally 1 3x-8<5x+5 -3x -3x -8<2x+5 -5 -5 Total Process If you are multiplying or dividing by a negative number, you have to 'flip the sign' on the inequalities. -8x-4>16x+4 The "Special Rule" -8x -8x -4<-2x+4 -4 2 -4 -8<-2x 4>x -2 -2 -2/3 ≤ x 5-4x≤2x + 9 -2/10≤x x<24 -x/2<12 x>-24 x>0 7x+4>8x-13 x<17 x≤-3/5 12+9x≤-x-18 x≤-3 x<-20 3(2x-4)>7x+8 x<-4 Sample Problems 5-4x≤2x/3 2/-x<12 3(2x-4)>7x+8 12+9x≤-x-18 -13<2x -13<2x -13/2<x 2 2 7x+4>8x-13 -1/3x + 4 < 4x Solve -1/3x + 4 < 4x *-3x *-3x 4>-12x 4>-12x /-12 /-12 -1/3<x 4x+7>3x-3 Solve 4x+7>3x-3 -3x -3x x+7>-3 x+7>-3 -7 -7 x>-10 Be sure to move the lesser variable.

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