Question

1. solve: 22 - 8x > 14x - 6 + 6x

Explanation:

Step1: Combine like terms on the right

First, we combine the \(14x\) and \(6x\) terms on the right side of the inequality. So, \(14x + 6x = 20x\), and the inequality becomes \(22 - 8x > 20x - 6\).

Step2: Add \(8x\) to both sides

To get all the \(x\) terms on one side, we add \(8x\) to both sides of the inequality. This gives us \(22 > 20x + 8x - 6\), which simplifies to \(22 > 28x - 6\).

Step3: Add 6 to both sides

Next, we add 6 to both sides to isolate the term with \(x\). So, \(22 + 6 > 28x\), which simplifies to \(28 > 28x\).

Step4: Divide both sides by 28

Finally, we divide both sides of the inequality by 28. Since 28 is positive, the direction of the inequality sign remains the same. So, \(\frac{28}{28} > \frac{28x}{28}\), which simplifies to \(1 > x\) or \(x < 1\).

Answer:

\(x < 1\)