Question

7-23. simplify each expression.
b. $\frac{1}{2}x + \frac{7}{12} + \frac{3}{5}x - \frac{2}{3}$

b. $5.3 - 2.8x - 7.1 + 3.9x$

Explanation:

Step1: Group like terms (first expression)

$\frac{1}{2}x + \frac{3}{5}x + \frac{7}{12} - \frac{2}{3}$

Step2: Combine x terms (find common denominator)

$\frac{5}{10}x + \frac{6}{10}x = \frac{11}{10}x$

Step3: Combine constant terms (find common denominator)

$\frac{7}{12} - \frac{8}{12} = -\frac{1}{12}$

Step4: Group like terms (second expression)

$-2.8x + 3.9x + 5.3 - 7.1$

Step5: Combine x terms

$(-2.8 + 3.9)x = 1.1x$

Step6: Combine constant terms

$5.3 - 7.1 = -1.8$

Answer:

First simplified expression: $\frac{11}{10}x - \frac{1}{12}$
Second simplified expression: $1.1x - 1.8$