Question

solve for ( x ) and graph the solution on the number line below.

( 16 < 3x + 7 leq 25 )

answer attempt 1 out of 5

inequality notation:

number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12

Explanation:

Step1: Subtract 7 from all parts

To isolate the term with \(x\), we subtract 7 from each part of the compound inequality. So we have \(16 - 7<3x + 7-7\leq25 - 7\), which simplifies to \(9 < 3x\leq18\).

Step2: Divide all parts by 3

To solve for \(x\), we divide each part of the inequality by 3. So \(\frac{9}{3}<\frac{3x}{3}\leq\frac{18}{3}\), which simplifies to \(3 < x\leq6\).

Answer:

Inequality Notation: \(3 < x\leq6\)

For the number line: We draw an open circle at \(x = 3\) (since \(x>3\), not including 3) and a closed circle at \(x = 6\) (since \(x\leq6\), including 6), then shade the region between 3 and 6.