Question

solve for $x$ and graph the solution on the number line below.
$-2leq -x + 4<3$
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Subtract 4 from all parts

Subtract 4 from each part of the compound - inequality:
\(-2-4\leq -x + 4-4<3 - 4\)
\(-6\leq -x<-1\)

Step2: Multiply all parts by - 1 and reverse the inequality signs

When we multiply or divide an inequality by a negative number, the direction of the inequality signs changes. So, \((-1)\times(-6)\geq(-1)\times(-x)>(-1)\times(-1)\)
\(6\geq x > 1\)
which can be written as \(1 < x\leq6\)

Answer:

Inequality Notation: \(1 < x\leq6\)
Number - Line: Mark an open circle at 1 (because \(x>1\)) and a closed circle at 6 (because \(x\leq6\)) and draw a line segment connecting them on the number - line.