Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number.

The phrase

The sum of a number and 6 means we add 6 to x:

x + 6

Twice the sum of a number and 6 means we multiply x + 6 by 2:

2(x + 6)

the difference of the number and 3 means we subtract 3 from x

x - 3

three times the difference of the number and 3 means we multiply x - 3 by 3:

3(x- 3)

The word

2(x + 6) = 3(x - 3)

Use the distributive property to multiply through:

2x + 12 = 3x - 9

Subtract 2x from each side:

2x - 2x + 12 = 3x - 2x - 9

x - 9 = 12

Add 9 to each side:

x - 9 + 9 = 12 + 9

x =

The phrase

*a number*means an arbitrary variable, let's call it x.The sum of a number and 6 means we add 6 to x:

x + 6

Twice the sum of a number and 6 means we multiply x + 6 by 2:

2(x + 6)

the difference of the number and 3 means we subtract 3 from x

x - 3

three times the difference of the number and 3 means we multiply x - 3 by 3:

3(x- 3)

The word

*is*means we set 2(x + 6) equal to 3(x - 3)2(x + 6) = 3(x - 3)

Use the distributive property to multiply through:

2x + 12 = 3x - 9

Subtract 2x from each side:

2x - 2x + 12 = 3x - 2x - 9

x - 9 = 12

Add 9 to each side:

x - 9 + 9 = 12 + 9

x =

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