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$Simplify the expression. Write your answers using integers or improper fractions. -(1)/(2)t+5(-t+(1)/(2)) Answer:$

Simplify the expression. Write your answers using integers or improper fractions. $\newline$ $-\frac{1}{2} t+5\left(-t+\frac{1}{2}\right)$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.

\newline

-\frac{1}{2} t+5\left(-t+\frac{1}{2}\right)

\newline

Answer:

Distribute and Multiply: Distribute the $5$ into the parentheses. $5 \times (-t) + 5 \times \left(\frac{1}{2}\right)$ = $-5t + \frac{5}{2}$
Combine Like Terms: Combine the like terms. $\newline$ $-\frac{1}{2}t - 5t + \frac{5}{2}$ $\newline$ To combine the like terms, we need to find a common denominator for the terms involving $t$ . $\newline$ The common denominator for $\frac{1}{2}$ and $5$ is $2$ , so we convert $-5t$ to $-\frac{10}{2}t$ . $\newline$ $-\frac{1}{2}t - \frac{10}{2}t$
Add and Convert to Fraction: Add the terms involving $t$ . $-\left(\frac{1}{2}\right)t - \left(\frac{10}{2}\right)t$ $= -\left(\frac{1 + 10}{2}\right)t$ $= -\left(\frac{11}{2}\right)t$
Add Constant Term: Add the constant term to the expression. $\newline$ $-\frac{11}{2}t + \frac{5}{2}$ $\newline$ This is the simplified expression.

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