Questions: Solve the compound inequality. -26 ≤ 4x-6<2 Graph the solution on the number line.

Solution Steps

The given compound inequality is: \[ -26 \leq 4x - 6 < 2 \]

First, we need to isolate the variable \( x \) in the middle. Start by adding 6 to all parts of the inequality: \[ -26 + 6 \leq 4x - 6 + 6 < 2 + 6 \] \[ -20 \leq 4x < 8 \]

Next, divide all parts of the inequality by 4 to solve for \( x \): \[ \frac{-20}{4} \leq \frac{4x}{4} < \frac{8}{4} \] \[ -5 \leq x < 2 \]

To graph the solution \(-5 \leq x < 2\) on the number line:

• Draw a closed circle at \( -5 \) to indicate that \( x \) can be equal to \(-5\).
• Draw an open circle at \( 2 \) to indicate that \( x \) cannot be equal to \( 2 \).
• Shade the region between \(-5\) and \(2\) to represent all the values \( x \) can take.

Final Answer