Question

Y = |x-5| + |x+5| if x<-5

Answer 1

• Answer: Y = -2x,

Hence, Y = -2x, For x < -5, The Function Y = | x - 5 | + | x + 5 |

Therefore, For: x < -5, The Function: Y = | x - 5 | + | x + 5 |

Simplifies to: Y = -2x

• Explanation:

• ANALYSIS:

To solve the problem, We need to consider the definition of the ABSOLUTE VALUE FUNCTION and the given condition: x < -5

We will break the absolute value expressions into their respective cases and simplify the equation.

• BREAK THE ABSOLUTE VALUE EXPRESSIONS:

Since: x < -5, We now have:

x - 5 < 0 and x + 5 < 0

• So, The absolute value expressions can be written as:

| x - 5 | = -(x - 5) and | x + 5 | = -(x + 5)

• Now, we substitute these expressions into the equation:

Y = -(x - 5) + ( -(x + 5))

• Simplify:

Y = -x + 5 - x - 5

• Combine Like Terms:

Y = -2x

• Draw the conclusion:

For x < -5, The Function Y = | x - 5 | + | x + 5 |

Simplifies to: Y = -2x

Hence, Y = -2x, For x < -5, The Function Y = | x - 5 | + | x + 5 |

I hope this helps you!