SOLUTION: 1.Ten less than the product of x and 9 is 8. 2.twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.

Algebra ->  Linear-equations -> SOLUTION: 1.Ten less than the product of x and 9 is 8. 2.twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.      Log On


   

Question 842061: 1.Ten less than the product of x and 9 is 8.
2.twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.
Answer by mxgirl22(39) About Me  (Show Source):
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Problem 1.) Ten less than the product of x and 9 is 8.

Problem 2.) Twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.

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Problem 1.) Ten less than the product of x and 9 is 8.

Step 1.) Interpret the words.

Ten less than(-10) the product(multiplication) of x and 9 is(=) 8.
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Problem 1.)

Step 2.) Put equation together.

9x-10=8
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Problem 1.)
Step 3.) Solve for "x".

9x-10=8

9x-10%2B10=8%2B10

9x=18

9x%2F9=18%2F9

x=2

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Problem 1.)
Step 4.) Check using x=2.

9x-10=8
9%282%29-10=8
18-10=8
8=8

Checks!
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Problem 1.)
Step 5.) Answer.
x=2

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Problem 2.) Twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.


Step 1.) Interpret the words.

Twice(multiply by 2) the difference(-) of a number(x) and 3 is(=) the same as 1 added(+) to three times the number(3x). Find the number.

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Problem 2.)
Step 2.) Put equation together.
2%28x-3%29=3x%2B1
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Problem 2.)
Step 3.) Solve for "x".

2%28x-3%29=3x%2B1
2x-6=3x%2B1
2x-2x-6=3x-2x%2B1
-6=x%2B1
-6-1=x%2B1-1
-7=x
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Problem 2.)
Step 4.) Check using x=-7.
2%28x-3%29=3x%2B1
2%28%28-7%29-3%29=3%28-7%29%2B1
-14-6=-21%2B1
-20=-20

Checks!

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Problem 2.)
Step 5.) Answer.
x=-7