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 \( 5(x+3) - 7(x-4) = 38 \), 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!