Question

Look at the verbal statement shown below. Seven decreased by the sum of eight and three times a number, z, is less than twice the difference between z and five. Which inequality can be used to solve for z? A. (3z+8)−7<2z−5 B. 7−(3z+8)<2z−5 C. 7−(3z+8)<2(z−5) D. (3z+8)−7<2(z−5)

Answer 1

The correct option is;

C. 7 - (3z + 8) < 2(z -5)

Explanation:

The verbal statement on the left hand side of the less than relationship, can be presented as follows;

7 - (8 + 3z)

Similarly, the verbal statement on the right hand side of the less than relationship, can be presented as follows;

2 × (z -5)

The combined statement can therefore, be presented as follows;

7 - (8 + 3z) < 2 × (z -5), which is the same as 7 - (3·z + 8) < 2(z -5) since we have;

(8 + 3z) is equivalent to (3z + 8), the order of arrangement of the terms within the parenthesis will not alter the total value of the terms within the parenthesis, since the signs remain unchanged

The correct option is therefore;

7 - (3z + 8) < 2(z -5).