Maggie needs to spend at least six hours each week practicing the piano. She has already practiced three and one fourth hours this week. She 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 she needs to practice on each of the two days.

three and one fourth + 2x ≤ 6
three and one fourth + 2x ≥ 6
three and one fourthx + 2 ≤ 6
three and one fourthx + 2 ≥ 6

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calculista calculista · Answer 1 · 2019-09-04T00:13:32+02:00

Answer:

three and one fourth + 2x ≥ 6

Step-by-step explanation:

Let

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

we know that

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

so

[tex]3\frac{1}{4}+2x\geq 6\ hours[/tex]

Convert mixed number to an improper fraction

[tex]3\frac{1}{4}\ hours=\frac{3*4+1}{4}=\frac{13}{4}\ hours[/tex]

substitute

[tex]\frac{13}{4}+2x\geq 6\ hours[/tex]

Subtract 13/4 both sides

[tex]2x\geq 6-\frac{13}{4}[/tex]

[tex]2x\geq \frac{11}{4}[/tex]

Divide by 2 both sides

[tex]x\geq \frac{11}{8}[/tex]

therefore

The minimum number of hours he needs to practice on each of the two days is [tex]\frac{11}{8}\ hours[/tex]