Solve and check your solution(s). If the equation has no real solution, so state.
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A) 16
C) 4

Question

Solve and check your solution(s). If the equation has no real solution, so state.
-
A) 16 
C) 4

Quizplus · Accepted Answer

To solve the equation, we need to isolate the variable on one side of the equation:

|x+1| = 2

We can split this into two separate cases:

Case 1: x+1=2 
x=1

Case 2: x+1=-2 
x=-3

Check: 
If we plug x=1 back into the original equation, we get:

|1+1| = 2 
2 = 2

This is true, so x=1 is a valid solution.

If we plug x=-3 back into the original equation, we get:

|-3+1| = 2 
2 = 2

This is also true, so x=-3 is a valid solution.

Therefore, the solution set is {-3,1}. The equation can be rewritten as $\sqrt{x} + 2\sqrt{x} = 6$. Simplifying, we get $3\sqrt{x} = 6$, which gives $\sqrt{x} = 2$. Squaring both sides, we get $x = 4$. Checking the solution, we see that $\sqrt{4} + 2\sqrt{4} = 2 + 4\cdot2 = 10$, which satisfies the equation. Therefore, the answer is Choice C.

Solve and Check Your Solution(s)