Solve the following absolute value inequality:|3𝑥−5|<6

Sure, here are the steps to solve the absolute value inequality |3x - 5| < 6:

Step 1: Set up two inequalities. The absolute value inequality |3x - 5| < 6 can be rewritten as two separate inequalities: 3x - 5 < 6 and -(3x - 5) < 6.

Step 2: Solve each inequality.

For 3x - 5 < 6, add 5 to both sides to get 3x < 11. Then, divide both sides by 3 to get x < 11/3.

For -(3x - 5) < 6, distribute the negative sign to get -3x + 5 < 6. Then, subtract 5 from both sides to get -3x < 1. Divide both sides by -3 to get x > -1/3. Remember, when you divide or multiply by a negative number, you must flip the inequality sign.

Step 3: Combine the solutions. The solution to the original inequality |3x - 5| < 6 is -1/3 < x < 11/3.