Question

solve for x and graph the solution on the number line below. -10 > x - 2 > -12 answer attempt 1 out of 3 < > ≤ ≥ or inequality notation: number line:

Explanation:

Step1: Add 2 to all parts of the compound inequality

To solve for \( x \) in the inequality \( -10 > x - 2 > -12 \), we add 2 to each part. This is based on the addition property of inequalities, which states that if \( a > b > c \), then \( a + d > b + d > c + d \) for any real number \( d \).

Adding 2 to each part:
\( -10 + 2 > x - 2 + 2 > -12 + 2 \)

Step2: Simplify each part

Simplify the left, middle, and right parts of the inequality:

• Left part: \( -10 + 2 = -8 \)
• Middle part: \( x - 2 + 2 = x \)
• Right part: \( -12 + 2 = -10 \)

So the simplified inequality is \( -8 > x > -10 \), which can also be written as \( -10 < x < -8 \) (since if \( a > b > c \), then \( c < b < a \)).

Answer:

Inequality Notation: \( -10 < x < -8 \)

For the number line:

• Draw a number line with marks at -12, -11, -10, -9, -8, -7, etc.
• Place open circles at -10 and -8 (since the inequality is strict, \( < \) and not \( \leq \) or \( \geq \)) to indicate that -10 and -8 are not included in the solution.
• Shade the region between -10 and -8 on the number line.