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Algebra 2 Inequalities











































If you have a math problem that has brackets and parenthsis which section do you work on first?

3(x - (2x-7)) less than or equal to 2(3x-5)

Comments for Algebra 2 Inequalities

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Aug 28, 2011
Solving an Inequality
by: Staff

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Part II

PEMDAS order of evaluation inside the square brackets [ ]: parentheses, exponents, MULTIPLICATION, division, addition, subtraction


3*[4x + (-1)*(2x-7)] ≤ 2*(3x-5)

3*[4x + (-1)*(2x) + (-1)*(-7)] ≤ 2*(3x-5)

3*[4x - 2x + 7] ≤ 2*(3x-5)

PEMDAS order of evaluation inside the square brackets [ ]: parentheses, exponents, multiplication, DIVISION, addition, subtraction

No division is required.

PEMDAS order of evaluation inside the square brackets [ ]: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

3*[4x - 2x + 7] ≤ 2*(3x-5)

3*[2x + 7] ≤ 2*(3x-5)

This concludes the evaluation of the expression inside the square brackets [ ].


Step 2: evaluate EXPONENTS


PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There are no exponents to evaluate.


Step 3: MULTIPLICATION


PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

3*[2x + 7] ≤ 2*(3x-5)

There are two places where multiplication must be completed: 3*[2x + 7] and 2*(3x-5)

3*[2x + 7] ≤ 2*(3x-5)


3*(2x) + 3*7 ≤ 2*(3x-5)

6x + 21 ≤ 2*(3x-5)

6x + 21 ≤ 2*(3x) + 2*(-5)

6x + 21 ≤ 6x - 10


Step 5: evaluate ADDITION & SUBTRACTION

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

No addition or subtraction is required.


Last Step: Solve for “x”

Subtract 6x from each side of the inequality


6x - 6x + 21 ≤ 6x - 6x - 10

0 + 21 ≤ 0 - 10

21 ≤ -10, not true for any value of x: the inequality has no solution



The final answer is: x ∈ Ø (Ø = null set. There is no value x for which the inequality is true. The inequality has no solution.)




Thanks for writing.

Staff
www.solving-math-problems.com


Aug 28, 2011
Solving an Inequality
by: S


Part I

The question:

If you have a math problem that has brackets and parenthsis which section do you work on first?


3[4x - (2x-7)] less than or equal to 2(3x-5)


The answer:

3[4x - (2x-7)] less than or equal to 2(3x-5)

3[4x - (2x-7)] ≤ 2(3x-5)

Use the PEMDAS order of operations.

PEMDAS order tells you what to do first, second, . . . etc.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction


Step 1: evaluate PARENTHESES


PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

There are three sets of parentheses to evaluate. Start with the innermost parentheses



(2x-7), no further simplification is possible inside the parentheses

(3x-5), no further simplification is possible inside the parentheses

3[4x - (2x-7)], simplify expression inside brackets.




PEMDAS applies inside the square brackets [ ], just as it applies to the overall expression

PEMDAS order of evaluation inside the square brackets [ ]: PARENTHESES, exponents, multiplication, division, addition, subtraction

(2x-7), no further simplification is possible inside the parentheses

PEMDAS order of evaluation inside the square brackets [ ]: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There are no exponents to evaluate.
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