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 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 eliminate the parentheses.
- \( 5(x + 3) = 5x + 15 \)
- \( -7(x - 4) = -7x + 28 \)

2. **Rewrite the Equation**: Substitute the distributed terms back into the equation.
- \( 5x + 15 - 7x + 28 = 38 \)

3. **Combine Like Terms**: Combine the terms on the left side of the equation.
- \( (5x - 7x) + (15 + 28) = 38 \)
- This simplifies to \( -2x + 43 = 38 \)

4. **Isolate the Variable**: Move constant terms to the right side by subtracting 43 from both sides.
- \( -2x = 38 - 43 \)
- \( -2x = -5 \)

5. **Solve for \( x \)**: Divide both sides by -2 to find \( x \).
- \( x = \frac{-5}{-2} \)
- \( x = \frac{5}{2} \) or \( 2.5 \)

6. **Check the Solution**: Substitute \( x = \frac{5}{2} \) back into the original equation to verify it.
- Calculate \( 5\left(\frac{5}{2} + 3\right) - 7\left(\frac{5}{2} - 4\right) \)
- \( = 5\left(\frac{5}{2} + \frac{6}{2}\right) - 7\left(\frac{5}{2} - \frac{8}{2}\right) \)
- \( = 5\left(\frac{11}{2}\right) - 7\left(\frac{-3}{2}\right) \)
- \( = \frac{55}{2} + \frac{21}{2} \)
- \( = \frac{76}{2} = 38 \)

The left side equals the right side, confirming that the solution is correct.

**Final Solution**: \( x = \frac{5}{2} \) or \( x = 2.5 \)