Question

Solving compound inequalities.

Answer 1

Procedure:

0.

`\begin{gathered} -x+5\le4 \\ -x+5\le4 \\ -x\le\: -1 \\ \mleft(-x\mright)\mleft(-1\mright)\ge\mleft(-1\mright)\mleft(-1\mright) \\ x\ge\: 1 \end{gathered}`

Answer in interval notation: [1, ∞)

2.

`\begin{gathered} 2x+3\ge-1 \\ 2x+3-3\ge\: -1-3 \\ 2x\ge\: -4 \\ (2x)/(2)\ge(-4)/(2) \\ x\ge\: -2 \end{gathered}`

Answer in interval notation: [-2, ∞)

Final answer:

`\lbrack1,\infty)`

Summary:

0. We isolated ,x ,from the inequality by subtracting, multiplying, and dividing different numbers.

,

1. We translated that inequality to interval notation