Solve the following inequalities.
1.) 3x + 2y < 6
2.) 2x^2 + y ≥ 2
I think for the first one the answer is 2 but the second one I'm not sure about?
the answer to the first one is not 2. What does that even mean?
3x + 2y < 6 means that
2y < 6-3x
y < 3 - 3/2 x
o, you graph the line y = 3 - 3/2 x and everything below that line is where y < 3 - 3/2 x. It's a region, not a number.
2x^2 + y > 2
y > 2 - 2x^2
So, everywhere above the parabola is the solution. See
http://www.wolframalpha.com/input/?i=y+%3E+2+-+2x%5E2
To solve inequalities, we need to determine the values of the variables that satisfy the inequality. I will solve each inequality step by step.
1.) 3x + 2y < 6 :
Step 1: Begin by subtracting 3x from both sides to isolate the y term:
2y < 6 - 3x
Step 2: Divide both sides of the inequality by 2 to isolate y:
y < (6 - 3x) / 2
So, the solution to the inequality is y < (6 - 3x) / 2.
2.) 2x^2 + y ≥ 2 :
Step 1: Begin by subtracting 2 from both sides to isolate the y term:
y ≥ 2 - 2x^2
Step 2: The inequality is already in the form y ≥ expression. However, if it were in the form y ≤ expression, we would need to multiply all terms by -1 to switch the inequality direction.
So, the solution to the inequality is y ≥ 2 - 2x^2.