Question

Suppose a friend is having difficulty solving -2(q-5) > -3(q+1). Explain how to solve the inequality, showing all the necessary steps and identifying the properties you would use.

Answer 1

Firstly, use the distributive property of multiplication (A(B + C) = A×B + A×C) on -2(q - 5) and -3(q + 1): $-2q+10>-3q-3$

Next, apply the addition property of equality (whatever you add to one side you have to add the same quantity to the other), and add 3q on both sides: $q+10>-3$

Lastly, apply the subtraction property of equality (whatever you subtract on one side you have to subtract the same amount on the other side), and subtract 10 on both sides. Your final answer will be $q>-13$