Algebra

Equations with xx on Both Sides

This type of equation requires you to collect like terms and isolate xx on one side of the equation.

Explanation of Equations with xx on Both Sides:

  1. Step 1: Move all xx-terms to one side of the equation using addition or subtraction.
  2. Step 2: Move all constant terms to the other side of the equation.
  3. Step 3: Simplify the equation to solve for xx.

Exercises and Answers:

  1. 2x+3=x+72x+3=x+7 → Answer: 44
  2. 5x−2=3x+85x−2=3x+8 → Answer: 55
  3. 4x+6=2x+124x+6=2x+12 → Answer: 33
  4. 7x−4=3x+167x−4=3x+16 → Answer: 55
  5. 6x+10=4x+206x+10=4x+20 → Answer: 55
  6. 8x−3=5x+98x−3=5x+9 → Answer: 44
  7. 9x+2=6x+149x+2=6x+14 → Answer: 44
  8. 3x+7=x+153x+7=x+15 → Answer: 44
  9. 10x−5=7x+1010x−5=7x+10 → Answer: 55
  10. 12x+4=8x+2012x+4=8x+20 → Answer: 44

Solving Equations with \( x \) on Both Sides

When solving equations with \( x \) on both sides, the goal is to collect like terms and isolate \( x \) on one side of the equation. Here’s how to do it:

  1. Step 1: Move all \( x \)-terms to one side of the equation using addition or subtraction.
  2. Step 2: Move all constant terms to the other side of the equation.
  3. Step 3: Simplify the equation to solve for \( x \).

Example: Solve \( 3x + 5 = 2x + 10 \).

  • Subtract \( 2x \) from both sides: \( 3x – 2x + 5 = 10 \).
  • Simplify: \( x + 5 = 10 \).
  • Subtract \( 5 \) from both sides: \( x = 5 \).

Exercises

Solve the following equations. Check your answers by clicking the “Check Answer” button.

1. Solve: \( 2x + 3 = x + 7 \)

2. Solve: \( 5x – 2 = 3x + 8 \)

3. Solve: \( 4x + 6 = 2x + 12 \)

4. Solve: \( 7x – 4 = 3x + 16 \)

5. Solve: \( 6x + 10 = 4x + 20 \)

6. Solve: \( 8x – 3 = 5x + 9 \)

7. Solve: \( 9x + 2 = 6x + 14 \)

8. Solve: \( 3x + 7 = x + 15 \)

9. Solve: \( 10x – 5 = 7x + 10 \)

10. Solve: \( 12x + 4 = 8x + 20 \)

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