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EQ: HOW CAN YOU CREATE AND SOLVE INEQUALITIES? I WILL CREATE AND SOLVE INEQUALITIES.
EXPRESSIONS, EQUATIONS AND
INEQUALITIESCh. 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
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-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 INEQUALITYNow 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 SOLUTIONSIs 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
25 + .5x < 60.
