a. 6x – 4 = -4 + 6x b. 4x – 6 = 4x + 3 c. -2x + 4 = -3x + 4
The Correct Answer and Explanation is:
Let’s solve each equation step by step:
a. 6x−4=−4+6x6x – 4 = -4 + 6x6x−4=−4+6x
- Start by simplifying both sides of the equation. In this case, the terms involving xxx are already on both sides, so we’ll move the terms with xxx to one side.
- Subtract 6x6x6x from both sides: 6x−4−6x=−4+6x−6x6x – 4 – 6x = -4 + 6x – 6x6x−4−6x=−4+6x−6x This simplifies to: −4=−4-4 = -4−4=−4 This is a true statement, which means the equation has infinitely many solutions. This is called an identity.
b. 4x−6=4x+34x – 6 = 4x + 34x−6=4x+3
- To eliminate xxx from one side, subtract 4x4x4x from both sides: 4x−6−4x=4x+3−4x4x – 6 – 4x = 4x + 3 – 4x4x−6−4x=4x+3−4x This simplifies to: −6=3-6 = 3−6=3 This is a contradiction. Since the statement is false, the equation has no solution.
c. −2x+4=−3x+4-2x + 4 = -3x + 4−2x+4=−3x+4
- Move the terms involving xxx to one side by adding 3x3x3x to both sides: −2x+4+3x=−3x+4+3x-2x + 4 + 3x = -3x + 4 + 3x−2x+4+3x=−3x+4+3x Simplifying both sides: x+4=4x + 4 = 4x+4=4
- Subtract 4 from both sides: x+4−4=4−4x + 4 – 4 = 4 – 4x+4−4=4−4 This simplifies to: x=0x = 0x=0 So, the solution to the equation is x=0x = 0x=0.
Summary:
- Equation (a) has infinitely many solutions.
- Equation (b) has no solution.
- Equation (c) has the solution x=0x = 0x=0.
