Question

question
solve for ( x ) and graph the solution on the number line below.
( x + 8 < 14 )
answer attempt 2 out of 2
inequality notation: ( x < 6 )
number line:
(number line image with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked)
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Explanation:

Step1: Subtract 8 from both sides

To solve the inequality \( x + 8 < 14 \), we subtract 8 from both sides of the inequality. This is based on the property of inequalities that allows us to add or subtract the same number from both sides without changing the direction of the inequality. So we have:
\( x + 8 - 8 < 14 - 8 \)

Step2: Simplify both sides

Simplifying the left - hand side, \( x+8 - 8=x \). Simplifying the right - hand side, \( 14 - 8 = 6 \). So the solution to the inequality is \( x<6 \).

For graphing on the number line:

• We draw an open circle at \( x = 6 \) (because the inequality is \( x<6 \), not \( x\leqslant6 \), so 6 is not included in the solution set).
• Then we draw an arrow to the left of 6 on the number line to represent all the numbers less than 6.

Answer:

The solution to the inequality \( x + 8<14 \) in inequality notation is \( x < 6 \). For the number line graph, there is an open circle at 6 and an arrow pointing to the left.