Solve the inequality. Graph the solution set and write it in interval notation.

- 3(x - 2) - 2x < - (4x + 6) + 3x

Write the answer in interval notation.
__ (Type your answer in interval notation.)

1 answer

Let's simplify the equation step by step:

-3(x - 2) - 2x < - (4x + 6) + 3x
Distribute the -3 and the -1 on the right side:
-3x + 6 - 2x < -4x - 6 + 3x
Combine like terms:
-5x + 6 < -x - 6
Add 5x to both sides:
6 < 4x - 6
Add 6 to both sides:
12 < 4x
Divide both sides by 4 (and flip the sign because we are dividing by a negative number):
3 > x
So, the solution to the inequality is x < 3.

The graph of this inequality would be an open circle at 3 on the number line, and shading to the left.

In interval notation, the solution set can be written as (-∞, 3).