# 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

 Aug 28, 2011 Solving an Inequality by: Staff ------------------------------------------------------ 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. ------------------------------------------------------