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Published byCody Richard Modified over 7 years ago

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**SOLVING INEQUALITIES Final Answer Step 1: Subtract 5 from both sides**

Step 2: Make a Clean Sweep Since -9 and -5 have the same sign, add their absolute values. +5 – 5 equals 0, leaving “x” all by itself=) Since the numbers are both negative, the answer is negative. Final Answer

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**SOLVING INEQUALITIES Final Answer Step 1: Divide both sides by -5**

Divide by -5 because: -5 and x are involved in multiplying… The opposite of multiplying is dividing Step 2: Make sure to change inequality sign Change inequality sign whenever MULTIPLYING OR DIVIDING by a NEGATIVE number=) Step 3: Make a Clean Sweep When dividing a negative number by a negative number, the answer is positive. The -5’s divide out, leaving “x” by itself. Final Answer

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**The 7’s divide out, leaving “x” by itself.**

SOLVING INEQUALITIES Multiply both sides by 7 because: 7 and b are involved in division… The opposite of dividing is multiplying. Step 1: Multiply both sides by 7 Step 2: Make a Clean Sweep A negative times a positive equals a negative so -4 times 7 is -28. The 7’s divide out, leaving “x” by itself. Final Answer

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**The -4’s divide out, leaving “x” by itself.**

SOLVING INEQUALITIES Step 1: Multiply both sides by -4 Multiply both sides by – 4 because: -4 and w are involved in division… The opposite of dividing is multiplying Step 2: Make sure to change inequality sign Change inequality sign whenever MULTIPLYING OR DIVIDING by a NEGATIVE number=) Step 3: Make a Clean Sweep A positive times a negative equals a negative. 8 times -4 is -32. The -4’s divide out, leaving “x” by itself. Final Answer

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**SOLVING INEQUALITIES Final Answer Step 1: Subtract 2 from both sides**

Perform adding and subtracting first when solving 2-step inequalities=) +2 -2 =0, leaving “4c” by itself. 30 – 2 = 28 Subtract 2 from both sides because: 2 is involved addition and the opposite of adding is subtracting=) Step 2: Divide both sides by 4 Divide by 4 because: 4 and c are involved in multiplying… The opposite of multiplying is dividing Step 3: Make a Clean Sweep 28 divided by 4 equals 7. Final Answer The 4’s divide out, leaving “c” by itself.

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**SOLVING INEQUALITIES Final Answer Step 1: Add 9 to both sides**

Perform adding and subtracting first when solving 2-step inequalities=) -9 +9 =0, leaving “-3d” by itself. = 21 Add 9 to both sides because: 9 is involved subtraction and the opposite of subtracting is adding=) Change inequality sign whenever MULTIPLYING OR DIVIDING by a NEGATIVE number=) Step 2: Divide both sides by -3 Divide by -3 because: -3 and d are involved in multiplying… The opposite of multiplying is dividing Step 3: Make a Clean Sweep A positive divided by a negative equals a negative 21 divided by -3 equals -7. Final Answer The -3’s divide out, leaving “d” by itself.

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**The -4’s divide out, leaving “y” by itself.**

SOLVING INEQUALITIES Step 1: Combine Like Terms 3y and -7y are like terms. Since 3y and -7y have opposite signs, we subtract the coefficients. (3 and -7 are the coefficients) The answer keeps the sign of the integer with the larger absolute value Add 1 to both sides because: 1 is involved subtraction and the opposite of subtracting is adding=) Step 2: Add 1 to Both Sides =32 -1 +1 =0, leaving “-4y” by itself. We change inequality sign whenever we MULTIPLY OR DIVIDE by a NEGATIVE number=) Step 3:Divide by 4 & Make a Clean Sweep A positive divided by a negative equals a negative. 32 divided by -4 equals -8. The -4’s divide out, leaving “y” by itself. Final Answer

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**The 10’s divide out, leaving “a” by itself.**

SOLVING INEQUALITIES Step 1: Combine Like Terms 9 and 1 are both integers so we add them =10 8a and 2a are like terms so we add the coefficients =10 Step 2: Divide both sides by 10 Divide by 10 because: 10 and a are involved in multiplying… The opposite of multiplying is dividing Step 3: Make a Clean Sweep 10 divided by 10 equals 1. The 10’s divide out, leaving “a” by itself. Final Answer

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**SOLVING INEQUALITIES Final Answer Step 1: Subtract 2 from both sides**

Perform adding and subtracting first when solving 2-step inequalities=) Step 1: Subtract 2 from both sides Since -7 and -2 have the same sign, add their absolute values. =0, leaving “x/6” by itself. Since the numbers are both negative, the answer is negative. Multiply by 6 because: 6 and x are involved in dividing… The opposite of dividing is multiplying Step 2: Multiply both sides by 6 Step 3: Make a Clean Sweep A negative times a positive equals a negative. -9 times 6 = -54 6 divided by 6 is 1. 1x=x Final Answer

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**-5 + 5 =0, leaving “x/-4” by itself.**

SOLVING INEQUALITIES Perform adding and subtracting first when solving 2-step inequalities=) Step 1: Add 5 to both sides 5 + 5 = 10 =0, leaving “x/-4” by itself. Multiply by -4 because: -4 and x are involved in dividing… The opposite of dividing is multiplying Step 2: Multiply both sides by -4 Step 3: Make a Clean Sweep We change inequality sign whenever we MULTIPLY OR DIVIDE by a NEGATIVE number=) A positive times a negative equals a negative. 10 times -4 = -40 4 divided by 4 is 1. 1x=x Final Answer

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**SOLVING INEQUALITIES Final Answer Step 2: Subtract 5 from both sides.**

Step 1: Distribute the negative sign to each term inside the parenthesis. Another way to write the negative sign is as a -1=) Step 2: Subtract 5 from both sides. = 10 =0, leaving “-1b” by itself. Step 3: Divide both Sides by -1 We change inequality sign whenever we MULTIPLY OR DIVIDE by a NEGATIVE number=) Step 4: Make a Clean Sweep A positive divided by a negative equals a negative. 10 divided by -1 equals -10 The -1’s divide out, leaving “b” by itself. Final Answer

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