Question

question solve for x and graph the solution on the number line below. 3 < x - 5 answer attempt 2 out of 2 < > ≤ ≥ or inequality notation: x > 8 number line: number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, arrows, green dots at 0 and 8 submit answer

Explanation:

Step1: Add 5 to both sides

To solve the inequality \( 3 < x - 5 \), we add 5 to both sides of the inequality. This is done to isolate the variable \( x \). The addition property of inequalities states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same. So, we have:
\( 3 + 5 < x - 5 + 5 \)

Step2: Simplify both sides

Simplifying the left - hand side: \( 3+5 = 8 \).
Simplifying the right - hand side: \( x-5 + 5=x \) (because \(-5 + 5=0\)).
So, the inequality simplifies to \( 8 < x \), which can be rewritten as \( x>8 \).

For graphing the solution on the number line:

• We look at the number line provided. The solution is \( x > 8 \), which means all real numbers greater than 8.
• On the number line, we use an open circle at 8 (because 8 is not included in the solution, since the inequality is strict, \( x>8 \) not \( x\geq8 \)) and draw an arrow to the right of 8 to represent all numbers greater than 8.

Answer:

Inequality Notation: \( x > 8 \)
For the number line: Place an open circle at 8 and draw an arrow pointing to the right (towards positive infinity) to represent all values of \( x \) such that \( x>8 \).