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$Simplify the expression. Write your answers using integers or improper fractions. -(5)/(2)((3)/(2)c+c+4)-c Answer:$

Simplify the expression. Write your answers using integers or improper fractions. $\newline$ $-\frac{5}{2}\left(\frac{3}{2} c+c+4\right)-c$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

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

\newline

-\frac{5}{2}\left(\frac{3}{2} c+c+4\right)-c

\newline

Answer:

Distribute Negative Fraction: Distribute the negative fraction across the terms inside the parentheses. $\newline$ We have the expression: $-(\frac{5}{2})((\frac{3}{2})c + c + 4)$ $\newline$ Distribute $-(\frac{5}{2})$ to each term inside the parentheses. $\newline$ $-(\frac{5}{2}) \times (\frac{3}{2})c - (\frac{5}{2}) \times c - (\frac{5}{2}) \times 4$
Simplify Multiplication: Simplify the multiplication of the fractions and the whole number. $\newline$ Multiply the coefficients of $c$ and simplify the multiplication with the whole number. $\newline$ $-(\frac{15}{4})c - (\frac{5}{2})c - (\frac{20}{2})$
Convert to Improper Fraction: Convert the mixed number to an improper fraction for easier addition/subtraction. $\newline$ Since $(\frac{5}{2})c$ is the same as $(\frac{10}{4})c$ , we can combine it with $-(\frac{15}{4})c$ . $\newline$ $-(\frac{15}{4})c - (\frac{10}{4})c - 10$
Combine Like Terms: Combine like terms. $\newline$ Add the coefficients of $c$ and subtract the whole number. $\newline$ $-\left(\frac{15}{4} + \frac{10}{4}\right)c - 10$ $\newline$ $-\left(\frac{25}{4}c\right) - 10$
Subtract $c$ : Subtract $c$ from the result of Step $4$ . $\newline$ We have the term $-c$ to subtract from our expression. $\newline$ $-\left(\frac{25}{4}\right)c - 10 - c$ $\newline$ Since $c$ is the same as $\left(\frac{4}{4}\right)c$ , we can write $-c$ as $-\left(\frac{4}{4}\right)c$ . $\newline$ $-\left(\frac{25}{4}\right)c - 10 - \left(\frac{4}{4}\right)c$
Combine c Terms: Combine the c terms. $\newline$ Add the coefficients of c. $\newline$ $-\left(\frac{25}{4}c\right) - \left(\frac{4}{4}c\right) - 10$ $\newline$ $-\left(\frac{25}{4} + \frac{4}{4}\right)c - 10$ $\newline$ $-\left(\frac{29}{4}c\right) - 10$
Final Simplified Expression: Write the final simplified expression. $\newline$ The expression is now simplified to: $\newline$ $-\left(\frac{29}{4}c\right) - 10$