Eugene and Wes are solving the inequality \(132-4x\le36\). Each begins by subtracting 132 from both sides to get \(-4x\le-96\), and then each divides both sides by-4. Eugene gets \(x\le24\) and Wes gets \(x\ge24\), however. Always happy to offer advice, Alex now suggests to Eugene and Wes that answers to inequalities can often be checked by substituting \(x=0\) into both the original inequality and the answer. What do you think of this advice? Graph each of these answers on a number line. \linebreak

(Continuation) After hearing Alex’s suggestion about using a test value to check an in- equality, Cameron suggests that the problem could have been done by solving the equation \(132-4x=36\) first. Complete the reasoning behind this strategy.\linebreak

(Continuation) Deniz, who has been keeping quiet during the discussion, remarks, “The only really tricky thing about inequalities is when you try to multiply them or divide them by negative numbers, but this kind of step can be avoided altogether. Cameron just told us one way to avoid it, and there is another way, too.” Explain this remark by Deniz.\linebreak

Eugene and Wes are solving the inequality \(132-4x\le36\). Each begins by subtracting 132 from both sides to get \(-4x\le-96\), and then each divides both sides by-4. Eugene gets \(x\le24\) and Wes gets \(x\ge24\), however. Always happy to offer advice, Alex now suggests to Eugene and Wes that answers to inequalities can often be checked by substituting \(x=0\) into both the original inequality and the answer. What do you think of this advice? Graph each of these answers on a number line. \linebreak

(Continuation) After hearing Alex’s suggestion about using a test value to check an in- equality, Cameron suggests that the problem could have been done by solving the equation \(132-4x=36\) first. Complete the reasoning behind this strategy.\linebreak

(Continuation) Deniz, who has been keeping quiet during the discussion, remarks, “The only really tricky thing about inequalities is when you try to multiply them or divide them by negative numbers, but this kind of step can be avoided altogether. Cameron just told us one way to avoid it, and there is another way, too.” Explain this remark by Deniz.\linebreak