Question

question
solve for x and graph the solution on the number line below.
14 > x + 3 > 8
answer attempt 1 out of 2
inequality notation:

Explanation:

Step1: Subtract 3 from all parts

To solve the compound inequality \(14 > x + 3 > 8\), we subtract 3 from each part of the inequality. This is based on the property of inequalities that if we perform the same operation (subtraction of 3 here) on all parts of a compound inequality, the inequality relations remain valid.

So, we have:

\(14 - 3>x + 3- 3>8 - 3\)

Step2: Simplify each part

Simplifying the left - hand side, \(14-3 = 11\); the middle part, \(x + 3-3=x\); and the right - hand side, \(8 - 3=5\).

After simplification, the inequality becomes \(11>x>5\), which can also be written as \(5 < x<11\) (since if \(a > b\) and \(b>c\), then \(c < b < a\)).

Answer:

Inequality Notation: \(5 < x<11\)