Question

Use the fact that f(x)=sqrt x is increasing on its domain to solve the inequality: sqrt (3x+1) > sqrt (x-5)

Answer 1

To solve the inequality √(3x+1) > √(x-5), we can square both sides of the equation and then simplify to find the solution.

Step-by-step explanation:

To solve the inequality √(3x+1) > √(x-5), we can square both sides of the equation. This is valid because both sides of the inequality are non-negative. Squaring the left side gives us (3x+1), and squaring the right side gives us (x-5). Since we want to find the values of x that satisfy the inequality, we can solve the resulting equation 3x+1 > x-5.

Subtracting x from both sides gives us 2x+1 > -5. Subtracting 1 from both sides gives us 2x > -6. Finally, dividing both sides by 2 gives us x > -3.

Therefore, the solution to the inequality is x > -3.

Answer 2

-3<x≤5

Step-by-step explanation:

√(3x+1)>√(x-5)

Square each one of the square roots. Then create 3 different inequality expressions and solve them/

1. 3x+1>x-5= x>-3

2. 3x+1≥0= x≥-1/3

3. x-5≥0= x≥5

From here I'm going to take the values that cover the most of the area in this expression which should be -3<x≤5.