Question

question 15. solve the inequality and graph the solution: $-4x + 7 geq 19$ undo clear all

Explanation:

Step1: Subtract 7 from both sides

$$-4x+7 - 7\geq19 - 7$$
$$-4x\geq12$$

Step2: Divide both sides by - 4 (and reverse the inequality sign)

When dividing an inequality by a negative number, the inequality sign flips.
$$\frac{-4x}{-4}\leq\frac{12}{-4}$$
$$x\leq - 3$$

Answer:

The solution of the inequality is \(x\leq - 3\). On the number - line, we use a closed circle at \(x = - 3\) (because the inequality includes equality, i.e., \(x=-3\) is part of the solution) and shade to the left (since \(x\) is less than or equal to \(-3\)).