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

Answer:

$x>6$

Step-by-step explanation:

So we have the inequality:

$-5\sqrt{x-2}$

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

$\sqrt{x-2} >2$

Square both sides:

$\sqrt{x-2}^2>2^2\\x-2>4$

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.