Solve for s. |s - 6| > 8 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Split Inequalities: We have the absolute value inequality |s - 6| > 8. We need to split this into two separate inequalities because the absolute value of a number is greater than 8 if the number itself is either greater than 8 or less than -8. So, we have two cases: 1. s - 6 > 8 2. s - 6 8. Add 6 to both sides to isolate s: s - 6 + 6 > 8 + 6 s > 14Solve Second Inequality: Solve the second inequality s - 6 8 is s 14.

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Solve for $s$ . $\newline$ |s - 6| > 8 $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form. $\newline$ ______

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Math Problems

Algebra 1

Solve absolute value inequalities

Full solution

Q. Solve for

s

\newline

|s - 6| > 8

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

______

Split Inequalities: We have the absolute value inequality |s - 6| > 8. We need to split this into two separate inequalities because the absolute value of a number is greater than $8$ if the number itself is either greater than $8$ or less than $-8$ . $\newline$ So, we have two cases: $\newline$ $1$ . s - 6 > 8 $\newline$ $2$ . s - 6 < -8
Solve First Inequality: Solve the first inequality s - 6 > 8. Add $6$ to both sides to isolate $s$ : s - 6 + 6 > 8 + 6 s > 14
Solve Second Inequality: Solve the second inequality s - 6 < -8. Add $6$ to both sides to isolate $s$ : s - 6 + 6 < -8 + 6 s < -2
Combine Inequalities: Combine the two inequalities into a compound inequality. $\newline$ The solution to the original inequality |s - 6| > 8 is s < -2 or s > 14.