the product of 3 and y is less than or equal to the sum of y and 6
3y <= y + 6
2y <= 6
To solve the equation, we need to translate the given information into an inequality.
"The product of 3 and y" can be written as 3y.
"The sum of y and 6" can be written as y + 6.
The inequality can be written as:
3y ≤ y + 6.
To isolate the variable, we need to move the terms containing y to one side of the inequality. Here's how we can do that step by step:
1. Subtract y from both sides of the inequality:
3y - y ≤ y - y + 6
2y ≤ 6.
2. Now, we can divide both sides of the inequality by 2 to solve for y:
2y/2 ≤ 6/2
y ≤ 3.
Therefore, the solution to the inequality is y ≤ 3.
To solve the inequality, let's break it down step by step:
1. Start with the given inequality: 3y ≤ y + 6.
2. First, let's get all the y terms on one side of the inequality. We can do this by subtracting y from both sides: 3y - y ≤ y - y + 6.
Simplifying, we get: 2y ≤ 6.
3. Now, we want to isolate y. Since 2 is multiplied by y, we can divide both sides by 2 to solve for y: (2y)/2 ≤ 6/2.
Simplifying, we get: y ≤ 3.
Therefore, the solution to the inequality is y ≤ 3.