you have been given the following equation to solve as a challenge by your friend please 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 eliminate the parentheses. \[ 5(x + 3) = 5x + 15 \] \[ -7(x - 4) = -7x + 28 \] So the equation becomes: \[ 5x + 15 - 7x + 28 = 38 \]

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

3. Isolate the variable: Move the constant term (43) to the right side by subtracting it from both sides. \[ -2x + 43 - 43 = 38 - 43 \] \[ -2x = -5 \]

4. Solve for \( x \): Divide both sides by -2 to isolate \( x \). \[ x = \frac{-5}{-2} \] \[ x = \frac{5}{2} \]

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

Since both sides equal 38, the solution \( x = \frac{5}{2} \) is verified.

Final Answer:

The solution to the equation is \( x = \frac{5}{2} \).