SOLUTION: two times a number plus 6 is three less than one fifth of the number.What is the number?

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Question 183013This question is from textbook texas algebra 1
: two times a number plus 6 is three less than one fifth of the number.What is the number? This question is from textbook texas algebra 1

Answer by MathGuyJoe(20) About Me  (Show Source):
You can put this solution on YOUR website!
In this case, we'll call our number 'n'. To convert the sentence into an equation, just break it up into parts:
"Two times a number plus 6" -> +2n+%2B+6+
"is" -> =
"Three less than one-fifth the number" -> +%281%2F5%29n+-+3+


Putting it all together you get:
+2n+%2B+6+=+%281%2F5%29n+-+3+


To get rid of the fraction, multiply both sides by 5:
+5%282n+%2B+6%29+=+5%28%281%2F5%29n+-+3%29+
+10n+%2B+30+=+1n+-+15+


To group the values, subtract 1n from both sides:
+10n+%2B+30+-+1n+=+1n+-+15+-+1n
+9n+%2B+30+=+-15+


Next, subtract 30 from both sides:
+9n+%2B+30+-+30+=+-15+-+30+
+9n+=+-45+


Lastly, divide both sides by 9:
+9n+%2F+9+=+-45+%2F+9+
+n+=+-5+


So our number is -5. To check our answer, let's substitute back into our orignal equation:
+2n+%2B+6+=+%281%2F5%29n+-+3
+2%28-5%29+%2B+6+=+%281%2F5%29%28-5%29+-+3
+-10+%2B+6+=+-1+-+3+
+-4+=+-4+ So it checks out.


Hope this helps. ~ Joe