You have been given the following equation to solve as a challenge by your friend. Create a list of steps that you could follow to find the solution. Make sure to include all steps in the correct order. 5(x+3)–7(x–4)=38
To solve the equation 5(x+3) - 7(x-4) = 38, you can follow these steps:
1. Distribute the 5 and the 7 into the parentheses:
- Multiply 5 by x: 5(x) = 5x
- Multiply 5 by 3: 5(3) = 15
- Multiply 7 by x: 7(x) = 7x
- Multiply 7 by -4: 7(-4) = -28
2. Write down the equation after distributing:
5x + 15 - 7x + 28 = 38
3. Combine like terms:
5x - 7x = -2x
15 + 28 = 43
The equation becomes: -2x + 43 = 38
4. Subtract 43 from both sides of the equation:
-2x + 43 - 43 = 38 - 43
-2x = -5
5. Divide both sides of the equation by -2 to isolate x:
-2x / -2 = -5 / -2
x = 5/2 or 2.5
Therefore, the solution to the equation 5(x + 3) - 7(x - 4) = 38 is x = 2.5.
Can u out that in a si pilar way
Sure! Here is a simplified version of the steps to solve the equation 5(x+3) - 7(x-4) = 38:
1. Distribute the 5 and 7 into the parentheses:
- 5(x) = 5x
- 5(3) = 15
- 7(x) = 7x
- 7(-4) = -28
2. Rewrite the equation after distributing:
5x + 15 - 7x + 28 = 38
3. Combine like terms:
5x - 7x = -2x
15 + 28 = 43
4. Simplify the equation:
-2x + 43 = 38
5. Subtract 43 from both sides:
-2x + 43 - 43 = 38 - 43
-2x = -5
6. Divide both sides by -2:
-2x / -2 = -5 / -2
x = 5/2 or 2.5
So the solution to the equation 5(x+3) - 7(x-4) = 38 is x = 2.5.
Can u make the equation shorter and. It super long
Certainly! Here is a shorter version of the steps to solve the equation 5(x+3) - 7(x-4) = 38:
1. Distribute the terms inside the parentheses:
5x + 15 - 7x + 28 = 38
2. Combine like terms:
-2x + 43 = 38
3. Simplify the equation:
-2x = -5
4. Divide both sides by -2:
x = 2.5
Therefore, the solution to the equation 5(x+3) - 7(x-4) = 38 is x = 2.5.
Shorter
Here is a further shortened version:
1. Distribute and simplify:
5x + 15 - 7x + 28 = 38
2. Combine like terms:
-2x + 43 = 38
3. Simplify the equation:
-2x = -5
4. Solve for x:
x = 2.5
Therefore, the solution to 5(x+3) - 7(x-4) = 38 is x = 2.5.
Now can u redo it
Understood! Here is a shorter version of the steps to solve the equation 5(x+3) - 7(x-4) = 38:
1. Distribute and simplify:
5x + 15 - 7x + 28 = 38
2. Combine like terms:
-2x + 43 = 38
3. Solve for x:
x = 2.5
Thus, the solution is x = 2.5.