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 $x$ .