Question

evaluate each algebraic expression for the given quantity.
5 $-6.2x + 1.4x$, $x = -9.3$
6 $3\frac{1}{2}x - 5\frac{1}{3}x$, $x = \frac{2}{5}$

Explanation:

Problem 5:

Step1: Combine like terms

First, combine the terms with \( x \) in the expression \( -6.2x + 1.4x \).
\( -6.2x + 1.4x = (-6.2 + 1.4)x = -4.8x \)

Step2: Substitute \( x = -9.3 \)

Now substitute \( x = -9.3 \) into the simplified expression \( -4.8x \).
\( -4.8 \times (-9.3) = 44.64 \)

Step1: Convert mixed numbers to improper fractions

Convert \( 3\frac{1}{2} \) to an improper fraction: \( 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \)
Convert \( 5\frac{1}{3} \) to an improper fraction: \( 5\frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{16}{3} \)

Step2: Combine like terms

Now, combine the terms with \( x \) in the expression \( \frac{7}{2}x - \frac{16}{3}x \).
Find a common denominator, which is 6.
\( \frac{7}{2}x = \frac{21}{6}x \) and \( \frac{16}{3}x = \frac{32}{6}x \)
So, \( \frac{21}{6}x - \frac{32}{6}x = \frac{21 - 32}{6}x = \frac{-11}{6}x \)

Step3: Substitute \( x = \frac{2}{5} \)

Substitute \( x = \frac{2}{5} \) into \( \frac{-11}{6}x \).
\( \frac{-11}{6} \times \frac{2}{5} = \frac{-11 \times 2}{6 \times 5} = \frac{-22}{30} = \frac{-11}{15} \)

Answer:

\( 44.64 \)

Problem 6: