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Solve for $t$ . $\newline$ $|-9t| < 18$ $\newline$ 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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Solve absolute value inequalities

Full solution

Q. Solve for

t

.

\newline

|-9t| < 18

\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

______

Absolute Value Inequality: We have the inequality: $\newline$ $|-9t| < 18$ $\newline$ First, we solve for $|-9t|$ . $\newline$ $|-9t| < 18$ means that the absolute value of $-9t$ is less than $18$ . $\newline$ This can be split into two separate inequalities: $\newline$ $-9t < 18$ and $-9t > -18$
Solving First Inequality: Now, we solve the first inequality: $\newline$ $-9t < 18$ $\newline$ To isolate $t$ , we divide both sides by $-9$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $t > -2$
Solving Second Inequality: Next, we solve the second inequality: $\newline$ $-9t > -18$ $\newline$ Again, we divide both sides by $-9$ , reversing the inequality sign. $\newline$ $t < 2$
Combining Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $-2 < t < 2$ $\newline$ This means that $t$ must be greater than $-2$ and less than $2$ .

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