What are the restrictions on x if the solution to the equation -4 - square root 4-x=6 involves real numbers?
-4 - √(4-x) = 6
-√(4-x) = 10
4-x = 100
x = -96
Unfortunately, this is not a solution, since
-4 - √(100) = -4-10 = -14, NOT 6
√100 is NOT ±10. √100 is 10. So, the equation as written has no real solutions
To find the restrictions on x for the solution to the equation involving real numbers, we need to consider the domain of the square root function.
In this case, the equation is:
-4 - √(4 - x) = 6
Let's solve it step by step:
Step 1: Move the -4 term to the right side:
-√(4 - x) = 6 + 4
Step 2: Simplify the equation:
-√(4 - x) = 10
Step 3: Square both sides of the equation to eliminate the square root:
(-√(4 - x))^2 = 10^2
(4 - x) = 100
Step 4: Solve for x by isolating x on one side:
- x = 100 - 4
Step 5: Simplify the equation further:
- x = 96
Step 6: Multiply both sides by -1 to isolate x:
x = -96
The solution to the equation is x = -96, which is a real number.
Therefore, there are no restrictions on x for the given equation to involve real numbers.
To find the restrictions on x for the given equation, we need to consider the domain of the square root function.
The equation is: -4 - √(4 - x) = 6
First, let's isolate the square root term by moving -4 to the right side:
√(4 - x) = 6 + 4
Simplifying the right side gives us:
√(4 - x) = 10
To eliminate the square root, we can square both sides:
(√(4 - x))^2 = 10^2
Simplifying further gives us:
4 - x = 100
Now, let's isolate the x term by moving 4 to the right side:
-x = 100 - 4
Simplifying gives us:
-x = 96
Multiplying both sides by -1 changes the sign of the inequality:
x = -96
Therefore, the solution to the equation involves real numbers when x = -96. There are no other restrictions on x.