Question

solve for x
$-5\sqrt{x+4}-4=-19$
$x=$
question 7
6 pts
solve for x
$-5\sqrt{2x-3}-1=64$
then find the value of $x-11$

Explanation:

Step1: Isolate the radical term

Add 4 to both sides:
$-5\sqrt{x+4} = -19 + 4$
$-5\sqrt{x+4} = -15$

Step2: Solve for the radical

Divide by -5:
$\sqrt{x+4} = \frac{-15}{-5}$
$\sqrt{x+4} = 3$

Step3: Eliminate the square root

Square both sides:
$(\sqrt{x+4})^2 = 3^2$
$x+4 = 9$

Step4: Solve for x

Subtract 4 from both sides:
$x = 9 - 4$
$x = 5$

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Step5: Isolate radical (second equation)

Add 1 to both sides:
$-5\sqrt{2x-3} = 64 + 1$
$-5\sqrt{2x-3} = 65$

Step6: Solve for the radical

Divide by -5:
$\sqrt{2x-3} = \frac{65}{-5}$
$\sqrt{2x-3} = -13$

Step7: Analyze the radical result

The square root of a real number cannot be negative, so this equation has no real solution for $x$. Thus, $x-11$ also has no real value.

Answer:

First equation: $x = 5$
Second equation: No real solution for $x$, so $x-11$ has no real value.