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115
x = -8.65x + 11 = -25 - 75x + 11 = -325x = -32 - 115x = -43x = -43/5x = -8.6Check:5(-8.6) + 11 = -32-43 + 11 = -32-32 = -32
Factor out the X^2. X^2(15X^2 - 115X +150) = 0 Use quadratic for that in parenthesis. Does not look pretty, but you have 1 zero. X^2 = 0 X = 0 -b +/- sqrt(b^2-4ac)/2a a = 15 b = - 115 c = 150 -(-115) +/- sqrt[(-115)^2 - 4(15)(150)]/2(15) 115 +/- sqrt(4225)/30 [115 +/- 65]/30 X = 0 X = 6 X = 50/30 = 5/3 Lucky that the number under the radical was so clean
A number line is used to draw the graph of the inequality. The graph of an inequality consists of the graphs of all its solutions.If you graph x < 5 on a number line, the solution is all real numbers to the left of 5. Use an open dot at 5, to indicate that 5 is not a solution.If you graph x > 5, the solution is all real numbers to the right of 5. Use an open dot at 5 to indicate that 5 is not a solution.If you graph x = 5, the solution is all real numbers to the right of 5, included 5. Use a closed dot at 5 to indicate that 5 is a solution.Inequalities that have the same solution set are called equivalent inequalities. Solving an inequality is a process of writing equivalent inequalities until you isolate the variable. To do this, you apply the addition, subtraction, multiplication, division and transitive properties.Examples:x + 9 -6 - 15-3x > -21 divide each side of the inequality by -3, and reverse the order of the inequality (that is, change the symbol of the inequality) ;x -4 and x > 4 the word and signals a conjunction.The solutions are all numbers that are solutions of both inequalities.Use an open dot at -4 and another open dot at 4. All numbers greater than -4 and less than 4 are solutions.x < -3 or x > 5 the word or signals a disjunction.The solutions are all numbers that are solutions of either inequality.Use an open dot at -3 and another open dot at 5. All numbers less than -3 and greater than 5 are solutions.Examples:-7 < 4 - x 1All numbers less than -0.4 and greater than 1 are solutions. Use an open dot at -0.4 and another open dot at 1.