in set builder notation how do you write the solutions of this inquality:
3x+10 greater than or equal to 4
{x| 3x+10 ≥ 4}
but, since 3x+10 ≥ 4 means that x ≥ -2, you probably want
{x| x ≥ -2}
Ah, inequality! The only time it's okay to be unequal. Alright, let me juggle my thoughts and give you the solution using set builder notation.
We have the inequality 3x + 10 ≥ 4. To find the solutions, we'll start by subtracting 10 from both sides to isolate the variable:
3x + 10 - 10 ≥ 4 - 10
Simplifying:
3x ≥ -6
Lastly, divide both sides by 3 to solve for x:
x ≥ -2
So, in set builder notation, the solution to the inequality 3x + 10 ≥ 4 is {x | x ≥ -2}. Now, that's a set of numbers that aren't clowning around!
To write the solution in set builder notation for the inequality 3x + 10 ≥ 4, we need to find the values of x that satisfy this inequality.
Step 1: Subtract 10 from both sides of the inequality:
3x + 10 - 10 ≥ 4 - 10
3x ≥ -6
Step 2: Divide both sides of the inequality by 3:
(3x)/3 ≥ (-6)/3
x ≥ -2
The solution set for the inequality 3x + 10 ≥ 4, in set builder notation, is {x | x ≥ -2}.
To write the solutions of the inequality 3x + 10 ≥ 4 using set builder notation, you need to follow these steps:
Step 1: Simplify the inequality if needed. In this case, the inequality is already in its simplest form.
Step 2: Solve the inequality for x. Start by subtracting 10 from both sides of the inequality:
3x + 10 - 10 ≥ 4 - 10
3x ≥ -6
Step 3: Divide both sides by 3 to isolate x:
(3x)/3 ≥ (-6)/3
x ≥ -2
Step 4: Write the solution in set builder notation. Since x is greater than or equal to -2, you can express the solution using set notation as:
{x | x ≥ -2}
In this notation, the curly braces {} denote a set, and the pipe | separates the variable (x) from the condition (x ≥ -2). This set represents all values of x that are greater than or equal to -2, which is the solution to the inequality.