Solve for x to determine if the equation has one, none, or infinite solutions. 3 (2x+2)-10×=-4×+6

Question

GPT-4o mini · Answer

Let's solve the equation step by step:

Given equation: $3 (2 x + 2) - 10 x = - 4 x + 6$

Step 1: Distribute the left side. $3 \times 2 x + 3 \times 2 - 10 x = - 4 x + 6$ $6 x + 6 - 10 x = - 4 x + 6$

Step 2: Combine like terms on the left side. $(6 x - 10 x) + 6 = - 4 x + 6$ $- 4 x + 6 = - 4 x + 6$

Step 3: Isolate variable terms. Now we see that both sides of the equation are identical: $- 4 x + 6 = - 4 x + 6$

This means that the equation is true for all values of $x$ .

Conclusion: The equation has infinite solutions. Every value of $x$ will satisfy the equation.