Problem Solving with Two-Step Equations Quick Check

Answer 1

Sure! Here’s a quick check on solving two-step equations. I’ll provide some example equations, and then we can go over the solutions.

Example Equations:

1. \( 2x + 3 = 11 \)
2. \( 5y - 7 = 18 \)
3. \( 3z + 4 = 10 \)
4. \( 7 - 2m = 1 \)
5. \( 4p + 5 = 29 \)

Instructions: Solve each equation for the variable.

Solutions:

1. \( 2x + 3 = 11 \)
   Subtract 3 from both sides:
   \( 2x = 8 \)
   Divide by 2:
   \( x = 4 \)

2. \( 5y - 7 = 18 \)
   Add 7 to both sides:
   \( 5y = 25 \)
   Divide by 5:
   \( y = 5 \)

3. \( 3z + 4 = 10 \)
   Subtract 4 from both sides:
   \( 3z = 6 \)
   Divide by 3:
   \( z = 2 \)

4. \( 7 - 2m = 1 \)
   Subtract 7 from both sides (note the sign change):
   \( -2m = -6 \)
   Divide by -2:
   \( m = 3 \)

5. \( 4p + 5 = 29 \)
   Subtract 5 from both sides:
   \( 4p = 24 \)
   Divide by 4:
   \( p = 6 \)

Feel free to check your answers or let me know if you need more examples or explanations!