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Simplify the expression.

-6+5(7)/(10)c-2(3)/(5)c+8

Simplify the expression. $\newline$ $-6+5 \frac{7}{10} c-2 \frac{3}{5} c+8$

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Simplify variable expressions involving like terms and the distributive property

Full solution

Q. Simplify the expression.

\newline

-6+5 \frac{7}{10} c-2 \frac{3}{5} c+8

Simplify Terms: Simplify the terms inside the parentheses. $\newline$ First, we need to simplify the expressions inside the parentheses by performing the multiplication. $\newline$ $5(7) = 35$ $\newline$ $2(3) = 6$ $\newline$ So the expression becomes: $\newline$ $-6 + \frac{35}{10}c - \frac{6}{5}c + 8$
Find Common Denominator: Simplify the fractions by finding a common denominator. $\newline$ The common denominator for the fractions $\frac{35}{10}c$ and $\frac{6}{5}c$ is $10c$ . $\newline$ So we rewrite the fractions with the common denominator: $\newline$ $\frac{35}{10}c = \left(\frac{35}{10}\right)c$ $\newline$ $\frac{6}{5}c = \left(\frac{12}{10}\right)c$ $\newline$ Now the expression is: $\newline$ $-6 + \left(\frac{35}{10}\right)c - \left(\frac{12}{10}\right)c + 8$
Combine Like Terms: Combine like terms. $\newline$ Now we combine the terms with $c$ and the constant terms separately. $\newline$ Combining the terms with $c$ : $\newline$ $\frac{35}{10}c - \frac{12}{10}c = \frac{35 - 12}{10} \times c$ $\newline$ $= \frac{23}{10}c$ $\newline$ Combining the constant terms: $\newline$ $-6 + 8 = 2$ $\newline$ So the expression now is: $\newline$ $2 + \frac{23}{10}c$

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