You practice playing your guitar every day. You spend 15 minutes practicing chords and the rest of the time practicing a new song. So the total number of minutes y you practice for the week is given by y=7(15+x), where x is the number of minutes you spend on practicing a new song.
a. Solve the equation for x.
b. How many minutes did you spend on a new song if you practiced 210 minutes last week? 245 minutes? 315 minutes?
is a: x=1/7y-15
a. y = 7(15 + x)
y = 105 + 7x
y - 105 = 7x
1/7y - 105/7 = x
X DOES NOT EQUAL 1/7y - 15. You didn't distribute the 7 to 15. Remember to distribute to all on the equation, not just the x!
b. 210 = 105 + 7x
105 = 7x
x = 105/7 = 15 minutes practicing new song
sorry. x does equal 1/7y - 15. but if you only spend 210 minutes practicing that one week, it is impossible for you to practice 245 or 315 minutes on the new song.
A: Solve for the equation for X.
Y=7(15+X)
Y=105+7X
Y-105=7X
Y/7-15=X or 1/7 Y-15=X
B: Plug in the number Y as 210, 245, 315
210=7(15+X)
210=105+7X
105=7X
15=X
[That was the example for if you practiced 210 minutes last week.]
245:
245=105+7X
140=7X
20=X
315:
315=105+7X
210=7X
30=X
2310
To solve the equation y=7(15+x) for x, we need to isolate x on one side of the equation.
a. Solve the equation for x.
Starting with the equation y=7(15+x), we begin by distributing the 7.
y = 105 + 7x
Next, we subtract 105 from both sides to isolate the term containing x.
y - 105 = 105 - 105 + 7x
Simplifying, we have:
y - 105 = 7x
Now, divide both sides by 7 to solve for x.
(y - 105)/7 = (7x)/7
Simplifying further,
x = (y - 105)/7
So, the equation is x = (y - 105)/7.
b. To find the number of minutes spent on a new song for different total practice times, we substitute the given values of y into the equation x = (y - 105)/7.
If y = 210 minutes:
x = (210 - 105)/7
x = 105/7
x = 15 minutes
If y = 245 minutes:
x = (245 - 105)/7
x = 140/7
x = 20 minutes
If y = 315 minutes:
x = (315 - 105)/7
x = 210/7
x = 30 minutes
So, if you practiced for 210 minutes last week, you spent 15 minutes on a new song. If you practiced for 245 minutes, you spent 20 minutes on a new song. And if you practiced for 315 minutes, you spent 30 minutes on a new song.