1). Solve each equation.

Question

17 = w - 4
2/3s = -6
1/3y + 1/4 = 5/12
x/8 - 1/2 = 6
5/6x - 1/3 = 5/2

2). In 1668, the Hope diamond was reduced from its original weight by about 45 carats, resulting in a diamond weighing about 67 carats. Write and solve an equation to find how many carats the original diamond weighed.

3). Write an equation to represent each relationship. The solve the equation.

Five times a number is 45.

My answers to these questions are the following:

1). 17 = w - 4, w = 19
2/3s = -6, s = 9
1/3y + 1/4 = 5/12, y = ?
x/8 - 1/2 = 6, x = ?
5/6x - 1/3 = 5/2, x = ?

2). w - 45 = 67, w = 112
The original weight of the diamond is about 112 carats.

3). 5 times (x) x = 45

Answer 1

2 and 3 are right.

1).
17 = w - 4, w = 19 Wrong. Add 4 to both sides of the equation.

2/3s = -6, s = 9 Wrong. Watch your sign.

1/3y + 1/4 = 5/12, y =
1/3y = 5/12 - 3/12
1/3y = 2/12
y = (2/12)/(1/3)
y = (2/12) * (3/1)
y = 6/12 = 1/2

Try the last two yourself.

x/8 - 1/2 = 6, x = ?
5/6x - 1/3 = 5/2, x = ?

Answer 2

1). 17 = w - 4, w = 21
2/3s = -6, s = -9
x/8 - 1/2 = 6, x = 52
5/6x - 1/3 = 5/2, x = ?

Answer 3

Yes, they are right.

5/6x - 1/3 = 5/2

5/6x = 5/2 + 1/3

5/6x = 15/6 + 2/6

5/6x = 17/6

x = (17/6) / (5/6)

x = (17/6) * (6/5)

x = 102/30 = 3 2/5

Check my arithmetic