Question

Graph the solution to the inequality. −5√x-2<−10 Drag the symbol to the correct location on the number line to graph the solution.

Answer 1

x > 6

Explanation:

Drag the fourth option onto 6 on the line. This is an open circle and points to the right, so it includes all values greater than 6 not including 6.

Answer 2

`x>6`

Explanation:

So we have the inequality:

`-5√(x-2)<-10`

Divide both sides by -5. Since we're dividing by a negative, the sign changes:

`√(x-2) >2`

Square both sides:

`√(x-2)^2>2^2\\x-2>4`

Add two to both sides:

`(x-2)+2>4+2\\x>6`

Therefore, x>6.

However, the expression under the square root cannot be negative. Therefore, there is another inequality. Set the expression under the square root to greater than or equal to 0:

`x-2\geq 0`

Add 2 to both sides:

`x\geq 2`

However, previously, we determined that x must be greater than 6. That overrules this, so we will ignore it.

Thus, the answer is:

`x>6`

So, drag the fourth option onto 6 on the line. This is an open circle and points to the right, so it includes all values greater than 6 not including 6.