i have a piece of wood 72 inches long i cut it into 3 peices. the 2nd peice is 6 inches longer than the 1st the third id 6 inches longer than the 2nd. write and equation and solve??

First you define the variable,

let x be the length of the first piece in inches.
Then make an equation using the variable to represent the given relations:
x + (x+6) + (x+6)+6 = 72
Collect like terms:
3x + 18 = 72
Solve for x:
3x = 72 - 18 = 54
x = 18
Finally, verify the answer using the given relations.
First piece = 18 inches
second piece = 24 inches
third piece = 30 inches
Total = 18+24+30 = 72 inches
The solution is correct.

thank you

Frist .18inches, 2nd .18+6=24inches,3rd. 24+6=30inches.

To check. 18 +24+ 30=72

To solve this problem, we can set up an equation based on the given information.

Let's use the variable "x" to represent the length of the first piece.

According to the problem, the second piece is 6 inches longer than the first piece. So, the length of the second piece will be x + 6.

Similarly, the third piece is 6 inches longer than the second piece. Therefore, the length of the third piece will be (x + 6) + 6, which simplifies to x + 12.

Now, we know that the sum of all three pieces should be 72 inches. Thus, the equation can be written as:

x + (x + 6) + (x + 12) = 72

To solve this equation, we can combine like terms:

3x + 18 = 72

Next, we can isolate the variable by subtracting 18 from both sides of the equation:

3x = 72 - 18
3x = 54

Finally, we divide both sides of the equation by 3 to solve for x:

x = 54 / 3
x = 18

Therefore, the length of the first piece is 18 inches. The second piece would be 18 + 6 = 24 inches, and the third piece would be 24 + 6 = 30 inches.