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: \[ x = \frac{5}{2} \quad \text{or} \quad 2.5 \]