Math with Mr. J: Solving Two-Step Equations

Introduction

• Focus on solving two-step equations.
• Objective: Isolate the variable.
  • Keep the equation balanced: whatever operation is done on one side, must be done on the other.

Key Steps for Solving Two-Step Equations

1. Isolate the variable:

   • Use the reverse order of operations.
   • Reverse the operations to undo them.

2. Maintaining balance in equations:

   • Whatever you do to one side of the equation, do to the other side.

Example Problems

Example 1: 2x - 6 = 10

1. Objective: Isolate x.
2. Reverse operations:
   • Step 1: Eliminate -6 by adding 6 to both sides.
     • Result: 2x = 16
   • Step 2: Divide by 2 to isolate x.
     • Result: x = 8
3. Check: Substitute x = 8 back into the original equation to verify.

Example 2: R/5 + 8 = 11

1. Objective: Isolate R.
2. Reverse operations:
   • Step 1: Subtract 8 from both sides.
     • Result: R/5 = 3
   • Step 2: Multiply by 5 to isolate R.
     • Result: R = 15
3. Check: Verify by substituting R = 15 back in.

Example 3: 7 = 16 - 3e

1. Objective: Isolate e.
2. Reverse operations:
   • Step 1: Subtract 16 from both sides.
     • Result: -9 = -3e
   • Step 2: Divide by -3 to isolate e.
     • Result: e = 3
3. Check: Confirm by substituting e = 3 back in.

Example 4: 2(Y - 8) = 24

1. Objective: Isolate Y.
2. Reverse operations:
   • Step 1: Divide by 2 to remove the multiplier outside the parenthesis.
     • Result: Y - 8 = 12
   • Step 2: Add 8 to both sides to isolate Y.
     • Result: Y = 20
3. Check: Validate by substituting Y = 20 back in.

Conclusion

• Key takeaway: Always use reverse operations to isolate the variable.
• Check each solution by substituting back into the original equation.

Thank you for watching! Until next time, peace.