-5z-2<3z+2
To solve the inequality -5z - 2 < 3z + 2, we need to isolate the variable z. Here's how to do it step by step:
Step 1: Remove any parentheses (there are none in this inequality).
Step 2: Combine like terms on each side of the inequality. To do this, add 5z to both sides:
-5z - 2 + 5z < 3z + 2 + 5z
-2 < 8z + 2
Step 3: Next, subtract 2 from both sides to isolate the term with the variable:
-2 - 2 < 8z + 2 - 2
-4 < 8z
Step 4: Now, divide both sides by 8 to solve for z. Remember, if you divide or multiply both sides by a negative number, the direction of the inequality will change. In this case, we divide by a positive number, so the inequality sign remains the same:
-4/8 < 8z/8
-1/2 < z
Therefore, the solution to the inequality -5z - 2 < 3z + 2 is z > -1/2.
Note: It's important to be careful when dividing or multiplying by a negative number in an inequality as it will result in reversing the inequality sign. This step is crucial and must be considered to ensure that the solution is correct.