Find all real number X Which satisfy the inequality 1/3(X+3)-1>1/5(X+6)
Pls I need answer with solution step
1 / 3 ( x + 3 ) - 1 > 1 / 5 ( x + 6 )
Multiply both sides by 15
1 / 3 ( x + 3 ) ∙ 15 - 1 ∙ 15 > 1 / 5 ( x + 6 ) ∙ 15
5 ( x + 3 ) - 15 > 3 ( x + 6 )
5 x + 15 - 15 > 3 x + 18
5 x > 3 x + 18
5 x - 3 x > 18
2 x > 18
x > 18 / 2
x > 9
To solve the inequality 1/3(X+3) - 1 > 1/5(X+6), we need to isolate the variable X.
Step 1: Multiply both sides of the inequality by 15 to eliminate the denominators:
15(1/3(X+3) - 1) > 15(1/5(X+6))
5(X+3) - 15 > 3(X+6)
Step 2: Simplify the equation:
5X + 15 - 15 > 3X + 18
5X > 3X + 18
Step 3: Move all terms containing X to one side of the inequality:
5X - 3X > 18
2X > 18
Step 4: Divide both sides of the equation by 2 to solve for X:
2X/2 > 18/2
X > 9
The solution to the inequality 1/3(X+3) - 1 > 1/5(X+6) is X > 9.
Therefore, any real number X that is greater than 9 will satisfy the inequality.