Question

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

Explanation:

Step1: Subtract 4 from all parts

$-2 - 4\leq -x+4 - 4<3 - 4$
$-6\leq -x < - 1$

Step2: Multiply all parts by -1 and reverse inequalities

When multiplying an inequality by a negative number, the direction of the inequality signs changes. So we get $6\geq x>1$, which can be rewritten as $1 < x\leq6$.

Answer:

Inequality Notation: $1 < x\leq6$
Number - Line: Draw a number line. Mark a open - circle at 1 (because 1 is not included in the solution set) and a closed - circle at 6 (because 6 is included in the solution set). Then shade the region between 1 and 6.