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Solving Inequalities
Algebra 1
• Solving inequalities is similar to solving linear
equations (ex. 2x+2=4), except for one small
but important detail: you flip the inequality
sign whenever you multiply or divide the
inequality by a negative number.
• Examples
-2x=4, answer: x=-2
-2x≥4, answer: x≤-2
Remember:
~The opposite of addition is subtraction
~The opposite of subtraction is addition
~The opposite of multiplication is division
~The opposite of division is multiplication
~When multiplying or dividing by a negative number,
the sign of the inequality switches
Please complete the following
questions for homework tomorrow.
Answer: m<9
~add 3 to both sides
Answer: a<3
~subtract 3 from both sides
Answer: x<1
~add 3 to both sides
Answer: t >-1
~Add 3 to both sides
Answer: y<-5
~Subtract 3 from both sides
Answer: t<-4
~Divide 2 from each side
Answer: k<2
~Divide by 6 on both sides
a
 2
3
Answer: a>6
~Multiply by -3 on both sides,
flip the inequality sign
2a
 4
5
Answer: a>-10
~Multiply each side by 5, then
divide each side by 2
2
6
x
3
Answer: a<-9
~Multiply each side by 3, then
divide each side by -2, switch
the inequality sign because we
are dividing by a negative
number
Answer: x>2
~Subtract 1 from each side,
then divide each side by 3
Answer: n>-2
Subtract 3 from each side then
divide each side by a -2, switch
the inequality sign because we
are dividing by a negative
number
Answer: r<-2
~Subtract 2 from each side
then divide by -3, switch the
inequality sign because we are
dividing by a negative number
x
1 2
3
Answer: x<-3
~Subtract 1 from each side,
then multiply each side by -3,
switch the inequality sign
because we are multiplying by
a negative number
x  (2)
 1
5
Answer: x<-7
Multiply each side by 5, then
subtract 2 from each side
Answer: n<-3
Answer: n-2<9
Helpful Websites
• http://www.youtube.com/watch?v=VgDe_D8o
jxw
• http://www.mathsisfun.com/algebra/inequalit
y-solving.html
• http://www.webmath.com/solverineq.html
SOL Regulations
• A.5 The student will solve multistep linear inequalities
in two variables, including
• a) solving multistep linear inequalities algebraically and
graphically;
• b) justifying steps used in solving inequalities, using
axioms of inequality and
• properties of order that are valid for the set of real
numbers and its subsets;
• c) solving real-world problems involving inequalities;
and
• d) solving systems of inequalities.