EXPRESSIONS, EQUATIONS AND INEQUALITIES Ch. 1.5 Solving Inequalities EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

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Lesson 1-5 Solving Inequalities September Objective:

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EXPRESSIONS, EQUATIONS AND INEQUALITIES Ch. 1.5 Solving Inequalities EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

BELL WORK EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING INEQUALITIES READ Just as properties of equality can be used to solve equations, properties of inequality can be used to solve inequalities. Properties of numbers and inequality can be used to solve an inequality be finding increasingly simpler inequalities that have the same solutions as the original inequality. For example, the addition property of equality states that if a = b, then a + c = b + c. In the addition property of inequality, the difference is that the equality symbol is replaced with an inequality symbol: if a < b, then a + c < b + c. EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING INEQUALITIES variables-expressions/cc-7th-two-step-inequalities/v/writing-and- using-inequalities-3https:// variables-expressions/cc-7th-two-step-inequalities/v/writing-and- using-inequalities-3 EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

WRITING AN INEQUALITY FROM A SENTENCE What inequality represents the sentence, “5 fewer than a number is at least 12.”? EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

WRITING AN INEQUALITY FROM A SENTENCE Now you try… What inequality represent the sentence, “The quotient of a number and 3 is no more than 15”? EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING AND GRAPHING AN INEQUALITY What is the solution? Graph it. -3(2x-5) + 1 > 4 EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING AND GRAPHING AN INEQUALITY Now you try… What is the solution? Graph it. -2(x+9)+5>3 EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

USING AN INEQUALITY A movie rental company offers two subscription plans. You can pay $36 a month and rent as many movies as desired, or you can pay $15 a month and $1.50 to rent each movie. How many movies must you rent in a month for the first plan to cost less than the second plan? EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

USING AN INEQUALITY Now you try… A digital music service offers two subscription plans. The first has a $9 membership fee and charges $1 per download. The second has a $25 membership few and charges $.50 per download. How many songs must you download for the second plan to cost less than the first plan? EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

NO SOLUTIONS OR ALL REAL NUMBERS AS SOLUTIONS Is the inequality always, sometimes, or never true? a.-2(3x+1) > -6x+7 b.5(2x-3)-7x < 3x+8 EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

NO SOLUTIONS OR ALL REAL NUMBERS AS SOLUTIONS Now you try… Is this always, sometimes, or never true? 4(2x-3) < 8(x+1) EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING AN AND INEQUALITY What is the solution of 7 < 2x+1 and 3x < 18 Graph the solution. EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING AN AND INEQUALITY Now you try… 5 < 3x-1 and 2x < 12 Graph the solution. EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING AN OR INEQUALITY What is the solution of 7 + k > 6 or 8 + k < 3? Graph the solution. EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

SOLVING AN OR INEQUALITY Now you try… What is the solution? Graph it. 7w+3 > 11 or 4w-1 < -13 EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.

CLOSURE (On your bell sheet) Create a word problem that can be solved using x < 60. EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.