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 \( x = 2.5 \)