Question

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

Answer 1

To solve the equation \( 5(x + 3) - 7(x - 4) = 38 \), you can follow these steps:

1. **Distribute the terms**: Apply the distributive property to both terms on the left side of the equation.
- Multiply \( 5 \) by \( (x + 3) \).
- Multiply \( -7 \) by \( (x - 4) \).

This gives you:
\[
5x + 15 - 7x + 28 = 38
\]

2. **Combine like terms**: Combine the \( x \) terms and the constant terms on the left side.
- Combine \( 5x \) and \( -7x \).
- Combine \( 15 \) and \( 28 \).

This simplifies to:
\[
-2x + 43 = 38
\]

3. **Isolate the variable**: To isolate \( x \), first subtract \( 43 \) from both sides of the equation.
\[
-2x = 38 - 43
\]
Simplifying this gives:
\[
-2x = -5
\]

4. **Solve for \( x \)**: Divide both sides by \( -2 \) to solve for \( x \).
\[
x = \frac{-5}{-2}
\]
Simplifying this gives:
\[
x = \frac{5}{2} \quad \text{or} \quad x = 2.5
\]

5. **Check your solution**: Substitute \( x = 2.5 \) back into the original equation to verify.
\[
5(2.5 + 3) - 7(2.5 - 4)
\]
Calculate:
\[
5(5.5) - 7(-1.5) = 27.5 + 10.5 = 38
\]
Since both sides of the original equation are equal to \( 38 \), the solution is verified.

So, the final answer is:
\[
x = \frac{5}{2} \quad \text{or} \quad 2.5
\]