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.

Question

5(x+3)−7(x−4)=38

Answer 1

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

1. Distribute the terms: Apply the distributive property to both terms on the left side of the equation. \[ 5(x) + 5(3) - 7(x) + 7(4) = 38 \] This simplifies to: \[ 5x + 15 - 7x + 28 = 38 \]

2. Combine like terms: Combine the \( x \) terms and the constant terms on the left side. \[ (5x - 7x) + (15 + 28) = 38 \] This simplifies to: \[ -2x + 43 = 38 \]

3. Isolate the variable term: Subtract 43 from both sides of the equation to isolate the term with \( x \). \[ -2x + 43 - 43 = 38 - 43 \] This gives: \[ -2x = -5 \]

4. Solve for \( x \): Divide both sides of the equation by -2 to find the value of \( x \). \[ x = \frac{-5}{-2} \] This simplifies to: \[ x = \frac{5}{2} \quad \text{or} \quad x = 2.5 \]

5. Write the final answer: Conclude with the solution to the equation. \[ x = 2.5 \]

Follow these steps in order to solve the equation successfully!