Questions: Solve the linear inequality and explain how you solved it. 2/3 x - 4 < -1/3 x - 5

Solution Steps

To solve the linear inequality \(\frac{2}{3} x - 4 < -\frac{1}{3} x - 5\), we need to isolate the variable \(x\) on one side of the inequality. This involves combining like terms and performing basic arithmetic operations to simplify the inequality.

1. Add \(\frac{1}{3} x\) to both sides to get all \(x\) terms on one side.
2. Combine the \(x\) terms.
3. Add 4 to both sides to isolate the \(x\) term.
4. Simplify the resulting inequality to find the solution for \(x\).

To solve the inequality \(\frac{2}{3} x - 4 < -\frac{1}{3} x - 5\), we first add \(\frac{1}{3} x\) to both sides to get all \(x\) terms on one side: \[ \frac{2}{3} x + \frac{1}{3} x - 4 < -5 \]

Combine the \(x\) terms: \[ \left(\frac{2}{3} + \frac{1}{3}\right)x - 4 < -5 \] \[ x - 4 < -5 \]

Add 4 to both sides to isolate the \(x\) term: \[ x - 4 + 4 < -5 + 4 \] \[ x < -1 \]

Final Answer