Question

solve the linear inequality. other than ∅, use interval notation to the solution set on a number line.
5(x + 5) ≥ 4(x - 4) + x
number line and multiple - choice options as shown in the image

Explanation:

Step1: Expand both sides

Expand the left side: \(5(x + 5)=5x + 25\)
Expand the right side: \(4(x - 4)+x = 4x-16 + x=5x-16\)
So the inequality becomes \(5x + 25\geq5x-16\)

Step2: Subtract \(5x\) from both sides

Subtract \(5x\) from both sides of the inequality: \(5x + 25-5x\geq5x-16 - 5x\)
Simplify to get \(25\geq - 16\)

Answer:

Since \(25\geq - 16\) is always true for all real numbers \(x\), the solution set is \((-\infty,\infty)\)