Question

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

Answer 1

Solve: 3(2x+2) − 10x = −4x + 6

Expand left: 6x + 6 − 10x = −4x + 6
Combine like terms: −4x + 6 = −4x + 6

Add 4x to both sides: 6 = 6, which is always true.

Conclusion: the equation is an identity — it is true for every x. There are infinitely many solutions (all real numbers).