three times the sum of a number and eight is four more than twice the sum of the number and six

Question

turn into numbers

 

Answer 1

3(x+8)=4+2*(x+6)

3x+24=4+2x+12

3x-2x=4+12-24

x=-8

 

Answer 2

Just write down what it says, but say it in "math".

 

First pick a variable to represent the number.  Let's call it x.

 

Now go step by step through the statement:

 

1. "the sum of a number and eight" -- that's x + 8

 

2. "three times the sum of a number and eight" -- That's 3 times what you got in step 1 -- 3(x + 8)

 

3. "is" -- "is" means "equals", so that's "="

 

4. "the sum of the number and six" -- that's x + 6

 

5. "twice the sum of the number and six" -- that's 2 times what you got in step 4:  2 (x + 6)

 

6. And finally, "four more than twice the sum of the number and six" -- that's what you got in step 5, with 4 added on:  2(x + 6) + 4

 

So that gives you an equation:

 

3(x + 8) = 2(x + 6) + 4

 

To solve it, first simplify:

3x + 24 = 2x + 12 + 4

3x + 24 = 2x + 16

 

Subtract 2x from both sides:

x + 24 = 16

 

Subtract 24 from both sides:

x = 16 - 24

x = -8

 

So the number is -8.