Question

Julian needs to spend at least seven hours each week practicing the drums. He has already practiced five and one third hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.

five and one third + 2x ≤ 7
five and one thirdx + 2 ≤ 7
five and one thirdx + 2 ≥ 7
five and one third + 2x ≥ 7

Answer 1

Answer: Fourth option is correct.

Explanation:

Since we have given that

Atleast number of hours each week practicing the drums = 7

Number of hours he already practiced =
`5(1)/(3)`

Let the number of hours left be x.

it splits the remaining practice time between the last two days.

So, it becomes,

`5(1)/(3)+2x\geq 7\\\\(16)/(3)+2x\geq 7\\\\2x\geq 7-(16)/(3)\\\\2x\geq (21-16)/(3)\\\\2x\geq (5)/(3)\\\\x\geq (5)/(6)`

Hence, Fourth option is correct.

Answer 2

five and one third + 2x ≥ 7

Explanation:

Let

x -----> the minimum number of hours he needs to practice on each of the two days

we know that

Julian needs to spend at least seven hours each week practicing the drums

so

`5(1)/(3)+2x\geq 7\ hours`

Convert mixed number to an improper fraction

`5(1)/(3)\ hours=(5*3+1)/(3)=(16)/(3)\ hours`

substitute

`(16)/(3)+2x\geq 7`

Subtract 16/3 both sides

`2x\geq 7-(16)/(3)`

`2x\geq (5)/(3)`

Divide by 2 both sides

`x\geq (5)/(6)`

therefore

The minimum number of hours he needs to practice on each of the two days is
`(5)/(6)\ hours`