Question

solve and graph the following inequality: 3 + 8x ≥ -7

Explanation:

Step1: Isolate the term with x

Subtract 3 from both sides of the inequality $3 + 8x\geq - 7$.
$3+8x - 3\geq - 7 - 3$
$8x\geq - 10$

Step2: Solve for x

Divide both sides of the inequality $8x\geq - 10$ by 8.
$x\geq-\frac{10}{8}=-\frac{5}{4}$

To graph $x\geq-\frac{5}{4}$ on a number - line:

1. Locate the point $x =-\frac{5}{4}=-1.25$ on the number - line.
2. Since the inequality is $x\geq-\frac{5}{4}$, we use a closed circle at $x =-\frac{5}{4}$ (because the value $x =-\frac{5}{4}$ is included in the solution set) and draw an arrow to the right to represent all the values of x that are greater than or equal to $-\frac{5}{4}$.

Answer:

Inequality: $x\geq-\frac{5}{4}$
Graph: A closed circle at $x = - 1.25$ on the number - line and an arrow pointing to the right.