Question

Matt practices his violin for at least 12 hours per week. He practices for three fourths of an hour each session. If Matt has already practiced 3 hours this week, what is the least number of sessions he must complete to meet his weekly practice goal? Write and solve an inequality.

Answer 1

We know that

• He practices 12 hours per week at least.

,

• Each session lasts three-fourths of an hour.

,

• He already practiced 3 hours this week. (There are 9 hours left)

Based on the given information, we can express the following

`3+(3)/(4)x\ge12`

Where x represents the number of sessions he must complete.

Let's solve for x

`\begin{gathered} (3)/(4)x\ge12-3 \\ (3)/(4)x\ge9 \\ x\ge(9\cdot4)/(3) \\ x\ge(36)/(3) \\ x\ge12 \end{gathered}`

He must have at least 12 sessions to reach his practice goal.