Question

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

Answer 1

Let's solve the equation step by step:

Given equation:
\[ 3(2x + 2) - 10x = -4x + 6 \]

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

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

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

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.