using the properties of inequality, Justify your steps in solving for the variable.
2/3x + 8 < 4
To solve the inequality 2/3x + 8 < 4, we can follow these steps:
1. Subtract 8 from both sides of the inequality to isolate the variable:
(2/3)x + 8 - 8 < 4 - 8
This simplifies to: (2/3)x < -4
2. Multiply both sides of the inequality by the reciprocal of the coefficient 2/3. Since the reciprocal of 2/3 is 3/2, we have:
(2/3)x * (3/2) < -4 * (3/2)
This simplifies to: x < -6
Therefore, the solution to the inequality is x < -6.