Question

4
drag the tiles to the boxes to form correct pairs.
match the pairs of equivalent expressions.
(-14 + \frac{3}{2}b) - (1 + \frac{8}{2}b) \t\t4b + \frac{13}{2}
(5 + 2b) + (2b + \frac{3}{2}) \t\t8b - 15
(\frac{7}{2}b - 3) - (8 + 6b) \t\t-\frac{5}{2}b - 11
(-10 + b) + (7b - 5) \t\t-15 - \frac{5}{2}b

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Explanation:

Step1: Simplify first expression

$$\begin{align*} (-14 + \frac{3}{2}b) - (1 + \frac{8}{2}b) &= -14 + \frac{3}{2}b - 1 - 4b\\ &= -15 + \frac{3}{2}b - \frac{8}{2}b\\ &= -15 - \frac{5}{2}b \end{align*}$$

Step2: Simplify second expression

$$\begin{align*} (5 + 2b) + (2b + \frac{13}{2}) &= 5 + \frac{13}{2} + 2b + 2b\\ &= \frac{10}{2} + \frac{13}{2} + 4b\\ &= 4b + \frac{23}{2} \end{align*}$$

Step3: Simplify third expression

$$\begin{align*} (\frac{7}{2}b - 3) - (8 + 6b) &= \frac{7}{2}b - 3 - 8 - 6b\\ &= -11 + \frac{7}{2}b - \frac{12}{2}b\\ &= -\frac{5}{2}b - 11 \end{align*}$$

Step4: Simplify fourth expression

$$\begin{align*} (-10 + b) + (7b - 5) &= -10 - 5 + b + 7b\\ &= 8b - 15 \end{align*}$$

Answer:

$(-14 + \frac{3}{2}b) - (1 + \frac{8}{2}b) \longleftrightarrow -15 - \frac{5}{2}b$
$(5 + 2b) + (2b + \frac{13}{2}) \longleftrightarrow 4b + \frac{23}{2}$
$(\frac{7}{2}b - 3) - (8 + 6b) \longleftrightarrow -\frac{5}{2}b - 11$
$(-10 + b) + (7b - 5) \longleftrightarrow 8b - 15$