Question

Write the expression without using absolute value symbols

|x+4| and x≥6

Answer 1

Answer: x + 4

Reason

The graph of y = |x+4| is V shaped with its lowest point when x = -4.

The left portion of the V shape is the line y = -(x+4) and occurs when x < -4

The portion on the right is the line y = x+4 and happens when x ≥ -4

Because x ≥ 6 is given to us, we're clear of the x ≥ -4 threshold. Therefore, we go for the equation y = x+4

|x+4| turns into x+4 when x ≥ 6

Answer 2

Expression is x+4

Explanation:

|x+4| and x≥6

If we want to write the expression |x+4| without using absolute value symbols, we need to consider two cases:

Case 1: x ≥ 0

In this case, |x+4| = x + 4.

So, the expression without using absolute value symbols is also x + 4.

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Case 2: x < 0

In this case, |x+4| = -(x+4) = -x - 4.

So, the expression without using absolute value symbols is -x - 4.

Therefore, the expression without using absolute value symbols is x + 4 if x ≥ 6, otherwise -x-4.