Question

3 times the absolute value of the quantity x plus 5 end quantity is equal to 18

Answer 1

Part A:** The absolute value equation representing the given description is
`\(3 |x + 5| = 18\).`

Part B:** The solution to the absolute value equation
`\(3 |x + 5| = 18\) is \(x = 1\) and \(x = -11\).`

**Part A: Writing the Absolute Value Equation**

The written description states "3 times the absolute value of the quantity
`\(x + 5\)` is equal to 18." Mathematically, this can be represented as:

`\[ 3 |x + 5| = 18 \]`

This equation conveys that the absolute value of
`\(x + 5\)` is multiplied by 3 and equated to 18.

**Part B: Solving the Absolute Value Equation**

To solve the absolute value equation
`\(3 |x + 5| = 18\)`, we need to isolate the absolute value term. First, divide both sides of the equation by 3:

`\[ |x + 5| = 6 \]`

Now, we consider both the positive and negative cases:

1.
`\(x + 5 = 6\)`

`\[ x = 1 \]`

2.
`\(x + 5 = -6\)`

`\[ x = -11 \]`

So, the solution set for the absolute value equation is
`\(x = 1\) and \(x = -11\).`