Solving Inequalities Algebra 1

Solving inequalities is similar to solving linear equations (ex 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.

Solve. m - 3 < 6

Answer: m<9 ~add 3 to both sides

Solve. 3 + a < 6

Answer: a<3 ~subtract 3 from both sides

Solve. -2 > x - 3

Answer: x<1 ~add 3 to both sides

Solve. t + (-3) > -4

Answer: t >-1 ~Add 3 to both sides

Solve. 3 + y < -2

Answer: y<-5 ~Subtract 3 from both sides

Solve. 2x < -8

Answer: t<-4 ~Divide 2 from each side

Solve. 12 > 6k

Answer: k<2 ~Divide by 6 on both sides

Solve.

Answer: a>6 ~Multiply by -3 on both sides, flip the inequality sign

Simplify.

Answer: a>-10 ~Multiply each side by 5, then divide each side by 2

Solve.

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

Solve. 3x - 1 > 5

Answer: x>2 ~Subtract 1 from each side, then divide each side by 3

Solve. -2n + 3 < 7

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

Solve. 8 < 2 - 3r

Answer: r<-2 ~Subtract 2 from each side then divide by -3, switch the inequality sign because we are dividing by a negative number

Solve.

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

Solve.

Answer: x<-7 Multiply each side by 5, then subtract 2 from each side

Write an inequality: A number is greater than -3.

Answer: n<-3

Write an inequality: 2 less than a number is less than 9.

Answer: n-2<9

Helpful Websites http://www.youtube.com/watch?v=VgDe_D8ojxw http://www.mathsisfun.com/algebra/inequality-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.