Question: Solve the inequality and write your answer in interval notation. $$-10 + 5x \leq 19x - 5$$

Solve the inequality and write your answer in interval notation.

$$-10 + 5x \leq 19x - 5$$

Solution

To solve the inequality \( -10 + 5x \leq 19x - 5 \), follow these steps: First, get all the terms involving \( x \) on one side and constant terms on the other side. Subtract \( 5x \) from both sides: \[ -10 \leq 19x - 5x - 5 \] Simplify by combining like terms: \[ -10 \leq 14x - 5 \] Add 5 to both sides to isolate the term with \( x \): \[ -10 + 5 \leq 14x \] Simplify the left side: \[ -5 \leq 14x \] Divide both sides by 14 to solve for \( x \): \[ x \geq -\frac{5}{14} \] In interval notation, the solution is \(\left[-\frac{5}{14}, \infty\right)\).