Question

solve for x and graph the solution on the number line below. -2 ≤ -x + 4 < 3 answer attempt 2 out of 10 inequality notation: 6 ≤ x < 1 number line:

Explanation:

Step1: Subtract 4 from all parts

Subtract 4 from each part of the compound - inequality $-2\leq -x + 4<3$.
We get $-2-4\leq -x + 4-4<3 - 4$, which simplifies to $-6\leq -x<-1$.

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

When we multiply each part of the inequality $-6\leq -x<-1$ by - 1, we must reverse the direction of the inequality signs.
So we have $6\geq x>1$, which can be written as $1 < x\leq6$.

Answer:

Inequality Notation: $1 < x\leq6$
Number - Line: Draw a number line. Mark a open - circle at 1 (since $x>1$) and a closed - circle at 6 (since $x\leq6$). Then shade the region between 1 and 6.