1. 4y + 3 <= y + 6
Answer: y <= 1
2. -2y > 2
Answer: y > -1
3. (y/3) < -1
Answer: y < -3
4. 3y <= 2y + 3
Answer: y <= 3
For the second one, I mean y < -1.
you are correct, with the update.
To solve each inequality, we need to isolate the variable on one side of the inequality sign. Let's solve each inequality step-by-step:
1. 4y + 3 <= y + 6
To isolate the variable 'y', let's first subtract 'y' from both sides of the inequality:
4y - y + 3 <= y - y + 6
Simplifying the equation:
3y + 3 <= 6
Next, let's subtract 3 from both sides of the inequality:
3y + 3 - 3 <= 6 - 3
Simplifying the equation:
3y <= 3
Finally, divide both sides of the inequality by 3 to solve for 'y':
(3y)/3 <= 3/3
Simplifying the equation:
y <= 1
Therefore, the solution is y <= 1.
2. -2y > 2
To isolate the variable 'y', let's first divide both sides of the inequality by -2. But remember, when dividing by a negative number, we must flip the inequality sign:
(-2y)/-2 < 2/-2
Simplifying the equation:
y < -1
Therefore, the solution is y < -1.
3. (y/3) < -1
To isolate the variable 'y', let's first multiply both sides of the inequality by 3:
3 * (y/3) < -1 * 3
Simplifying the equation:
y < -3
Therefore, the solution is y < -3.
4. 3y <= 2y + 3
To isolate the variable 'y', let's first subtract '2y' from both sides of the inequality:
3y - 2y <= 2y - 2y + 3
Simplifying the equation:
y <= 3
Therefore, the solution is y <= 3.
I hope the step-by-step solutions above are helpful! Let me know if you need further assistance.
To solve these inequalities, we need to isolate the variable y and determine the range of values that satisfy the given inequality. Here's how we can find the solutions step-by-step:
1. 4y + 3 <= y + 6
To isolate y, we can start by subtracting y from both sides of the inequality:
4y + 3 - y <= y + 6 - y
Simplifying the equation, we get:
3y + 3 <= 6
Next, we subtract 3 from both sides:
3y <= 6 - 3
Simplifying further:
3y <= 3
To solve for y, divide both sides of the equation by 3:
y <= 1
Therefore, the solution to the inequality is y <= 1.
2. -2y > 2
To isolate y, we need to divide both sides of the inequality by -2. However, since we are dividing by a negative number, we also need to reverse the inequality sign:
-2y/(-2) < 2/(-2)
Simplifying the equation, we get:
y < -1
So the solution to the inequality is y < -1.
3. (y/3) < -1
To isolate y, we can start by multiplying both sides of the inequality by 3 since we are dividing y by 3:
3 * (y/3) < -1 * 3
Simplifying the equation, we get:
y < -3
Hence, the solution to the inequality is y < -3.
4. 3y <= 2y + 3
To isolate y, we start by subtracting 2y from both sides of the inequality:
3y - 2y <= 2y + 3 - 2y
Simplifying the equation, we get:
y <= 3
Thus, the solution to the inequality is y <= 3.