Questions: Consider the following inequality: 3x-5+4>0

Transcript text: Consider the following inequality: \[ |3 x-5|+4>0 \] Step 1 of 2: Rewrite the inequality in standard form and determine if there is a solution.

Solution

Solution Steps

Step 1: Rewrite the inequality in standard form

The given inequality is: \[ |3x - 5| + 4 > 0 \]

To rewrite this in standard form, we need to isolate the absolute value expression: \[ |3x - 5| + 4 > 0 \] Subtract 4 from both sides: \[ |3x - 5| > -4 \]

Step 2: Determine if there is a solution

The absolute value of any expression is always non-negative, meaning: \[ |3x - 5| \geq 0 \]

Since \(|3x - 5|\) is always greater than or equal to 0, it will always be greater than -4. Therefore, the inequality \(|3x - 5| > -4\) is always true for all real numbers \(x\).