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$Solve for t. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. 12 t-2 < -5t+36$

Solve for $t$ . Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ 12t - 2 < -5t + 36

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Solve multi-step inequalities

Full solution

Q. Solve for

t

. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

\newline

12t - 2 < -5t + 36

Combine like terms: Combine like terms by moving all terms involving $t$ to one side of the inequality and constants to the other side. $\newline$ To do this, add $5t$ to both sides and add $2$ to both sides. $\newline$ 12t - 2 + 5t + 2 < -5t + 36 + 5t + 2 $\newline$ This simplifies to: $\newline$ 12t + 5t < 36 + 2
Simplify inequality: Simplify both sides of the inequality. $\newline$ Combine the $t$ terms on the left side and the constant terms on the right side. $\newline$ $12t + 5t = 17t$ $\newline$ $36 + 2 = 38$ $\newline$ So the inequality becomes: $\newline$ 17t < 38
Solve for $t$ : Solve for $t$ by dividing both sides of the inequality by $17$ .17t < 38t < \frac{38}{17}t < 2.235294117647059 (This is the decimal form, but we need to keep it as a fraction and reduce it to lowest terms.)
Reduce fraction: Reduce the fraction $\frac{38}{17}$ to its lowest terms. $\newline$ Since $38$ and $17$ have no common factors other than $1$ , the fraction is already in its simplest form. $\newline$ Therefore, t < \frac{38}{17}.

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