41-(2x+4)< or + to 2(x+1)+x
Use set-builder notation to describe the complete solution.
{x/x__ __}
To solve the inequality and express the solution in set-builder notation, follow these steps:
Step 1: Simplify the inequality
41 - (2x + 4) ≤ 2(x + 1) + x
First, simplify the expressions on both sides:
41 - 2x - 4 ≤ 2x + 2 + x
Combine like terms:
37 - 2x ≤ 3x + 2
Step 2: Isolate the variable
To isolate the variable (x), we need to move all terms containing x to one side of the inequality:
-2x - 3x ≤ 2 - 37
Combine like terms:
-5x ≤ -35
Step 3: Divide by the coefficient of x
To solve for x, divide both sides of the inequality by -5. Remember, when dividing/multiplying by a negative number, you must change the direction of the inequality:
-5x/-5 ≥ -35/-5
x ≥ 7
Step 4: Express the solution in set-builder notation
The solution to the inequality is all values of x that are greater than or equal to 7. We can express this as:
{x | x ≥ 7}
This set-builder notation means "the set of all values x such that x is greater than or equal to 7."