Solve the following inequality for z. Write your answer in simplest form.
62 - 7 > 8z + 2

z < 6

Step-by-step explanation:

62 - 7 > 8z + 2

To solve for z, we are going to follow the steps below;

62 - 7 > 8z + 2

55 > 8z + 2

subtract 2 from both-side of the inequality

55 - 2> 8z + 2 - 2

53  > 8z

Divide both-side of the inequality by 8

53/8   > 8z/8

(On the right-hand side of the inequality, 8 on the numerator will cancel-out 8 on the denominator leaving us with just z and on the right-hand side of the inequality 53 will be divided by 8)

53/8  > z

This implies z <

                    z < 6

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.