Question

2/3 of the sum of three times a number and six is 10. what is the number?

Answer 1

x=3

Explanation:

Write the equation first, 2/3(3x+6)=10

Distribute 2, 2(3x+6)/2

Which equals 6x+12/3=10

Then multiply 3 from both sides 6x+12=30

Subtract 12

6x=18

Divide 6 from both sides

x=3

Answer 2

9514 1404 393

Answer:

3

Explanation:

Let x represent the number. The problem statement tells you ...

2/3(3x +6) = 10

2x +4 = 10 . . . . . . use the distributive property

x +2 = 5 . . . . . . . . divide by 2

x = 3 . . . . . . . . . . .subtract 3

The number is 3.

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Comment on the solution

The above shows an "alternative" solution method. The more usual way this might be done is ...

2(3x +6) = 30 . . . . . multiply by 3 to clear fractions

6x +12 = 30 . . . . . . . eliminate parentheses

6x = 18 . . . . . . . . . . . subtract 12

x = 3 . . . . . . . . . . . . divide by 6