Solving Algebra Problem Write two Separate Inequalities - 550 Words

Solving Algebra Problem: Write two Separate Inequalities (Coursework Sample) Content: AlgebraNameInstitutionAlgebra 1 -12 12 + 4x 0First step: write as two separate inequalities-12 12 + 4x and12 + 4x 0Step two: solve both inequalities separately for the value of x-12 12 + 4x12 + 4x 0-12 -12 4x 4x -12-24 4x4x/4 -12/4-24/4 4x/4x -3-4 The compound inequality can be interpreted as-4 -3This can be rewritten as set notation showing intersection of sets{x: -4 x -3 }This is an intersection of intervals (-4, -3). This means that all the values between -4 and -3 are solutions to the compound inequality (Aufmann Lockwood, 2013).The graph on the number line will be:4857753695700038957252286000041910035242500270510024638000321945023876000351472523749000center2749550022860002768600018186402749550013430252863850094297528638500504190264795004762504000500087630035052000-4 -3 -2 -1 0 1 2 3 4All values within the thick line on the number line would solve the compound inequality. 2 12 à ¢Ã¢â€š ¬ x 15 or 7x à ¢Ã¢â€š ¬ 13 1First step is to solve both the inequalities separately12- x 157x à ¢Ã¢â€š ¬ 13 1-x 15 à ¢Ã¢â€š ¬ 127x 1 + 13-x 37x 14-x/- 1 3/-17x/7 14/7x - 3x 2Division of the inequality by a negative number leads to change of the inequality sign (Hansen, 2014). Hence, changed to when divided by - 1The compound inequality can be interpreted asx - 3 or x 2The set notation will be { x: x -3 or x 2 } showing union of sets.The values of x less than à ¢Ã¢â€š ¬ 3 satisfy the inequality or values of x le...