How do you solve and write the following in interval notation: $4\le 3-x<8$ ?

Janessa Olson
2022-07-04
Answered

How do you solve and write the following in interval notation: $4\le 3-x<8$ ?

You can still ask an expert for help

Jayvion Mclaughlin

Answered 2022-07-05
Author has **14** answers

Step 1

Isolate x in the middle interval by subtracting 3 from all 3 intervals

$4-3\le 3-3-x<8-3$

$\Rightarrow 1\le -x<5$

multiply all 3 intervals by - 1 remembering to reverse the inequality signs

$\Rightarrow -1\ge x>-5\leftarrow {\phantom{\rule{1ex}{0ex}}\text{reverse signs}}$

in interval notation as $\text{in interval notation as}\phantom{\rule{1ex}{0ex}}(-5,-1]$

Isolate x in the middle interval by subtracting 3 from all 3 intervals

$4-3\le 3-3-x<8-3$

$\Rightarrow 1\le -x<5$

multiply all 3 intervals by - 1 remembering to reverse the inequality signs

$\Rightarrow -1\ge x>-5\leftarrow {\phantom{\rule{1ex}{0ex}}\text{reverse signs}}$

in interval notation as $\text{in interval notation as}\phantom{\rule{1ex}{0ex}}(-5,-1]$

asked 2022-03-29

asked 2021-12-11

Solve p=2l+2w for w.

asked 2022-07-26

A coffee company wants a new flavor of Cajun. How many pounds of coffee worth $7 should be added to 10 pounds of coffee worth $3 to get a mixture worth $5 a pound?

asked 2022-08-31

Multiply. Write your answer as a mixed number in simplest form.

$2\frac{7}{9}\times 2\frac{1}{5}$

$2\frac{7}{9}\times 2\frac{1}{5}$

asked 2021-09-29

(a) What is the logical first step in solving the equation

$|2x-1|=5?$

(b) What is the logical first step in solving the inequality

$|3x+2|\le 8?$

(b) What is the logical first step in solving the inequality

asked 2022-05-11

How do you solve $\frac{x}{2}<\frac{5}{8}$ ?

asked 2022-02-04

How do you simplify $5(3x-4)-8(10-2x)$ ?