Question

Properties of EqualityUse properties to solve each equation for x.5. x + 9.8 = 14.2 6. 14x = 91 7. ⅓x = 24Like Terms Combine like terms in each expression8. ¼k + ¼m - ⅔k + 5/8m 9. -4b + 2w + (-4b) + 8w 10. 6 - 5z + 8 - 4z + 1

Answer 1

Question 5

x + 9.8 = 14.2

subtract 9.8 from both sides

x + 9.8 - 9.8 = 14.2 - 9.8

x = 4.4

Question 6

14x = 91

Divide both sides by coefficient of x

$\begin{gathered} \frac{14x}{14}\text{ =}\frac{91}{14} \\ \\ x\text{ = 6.5} \\ \end{gathered}$

Question 7

$\begin{gathered} \frac{1}{3}x\text{ =24} \\ \\ Mul\text{tiply both sides by 3} \\ 3\text{ x }\frac{1}{3}x\text{ = 24 x 3} \\ \\ x\text{ = 72} \end{gathered}$

Question 8

$\begin{gathered} \frac{1}{4}k\text{ + }\frac{1}{4}m\text{ -}\frac{2}{3}k\text{ + }\frac{5}{8}m \\ \\ \text{collect like terms} \\ \\ \frac{1}{4}k\text{ -}\frac{2}{3}k\text{ +}\frac{1}{4}m\text{ +}\frac{5}{8}m \\ solve\text{ }\frac{1}{4}k\text{ -}\frac{2}{3}k\text{ } \\ \Rightarrow\text{ }\frac{3k\text{ - 8k}}{12} \\ \Rightarrow\frac{-5k}{12} \\ \text{Also for the m coefficient} \\ \frac{1}{4}m+\text{ }\frac{5}{8}m \\ \Rightarrow\text{ }\frac{2m\text{ + 5m}}{8} \\ \frac{7m}{8} \end{gathered}$

$\begin{gathered} \text{Combining the m and k coeficient} \\ \frac{-5k}{12}+\frac{7m}{8} \end{gathered}$

Question 9

-4b +2w + (-4b) + 8w

=> -4b + 2w - 4b + 8w

collect like terms

=> -4b -4b + 2w + 8w

=> -8b + 10w

Question 10

6 - 5z + 8 - 4z + 1

collect the like terms

=> 6 + 8 + 1 - 5z - 4z

=> 15 - 9z