If −6<−4r+10≤2, what is the least possible value of 4r+3 ?
Notice that this question is asking for an expression instead of a variable, so manipulate the inequality to so that you get 4r+3 in the inequality. Treat each side of the inequality separately to avoidconfusion. Starting with the −6<−4r+10 part, multiply both sides of the inequality by −1, remembering to switch the sign, to get 6>4r− 10 . Add 13 to each side to get 19>4r+3. Then solve the right side of the inequality. Again, multiply both sides of the inequality by −1, switching the sign to get 4r−10≥−2. Now add 13 to each side of the equation: 4r+3≥11. Finally, combine the equations to get the range for 4r+3. Since the question asks for the least possible value of the expression, 11, (D), is the correct answer to the question. If you see the answer before the last step above, you don't need to combine the equations.