Question

4
drag the tiles to the boxes to form correct pairs.
match the pairs of equivalent expressions.
$\left(-14 + \frac{3}{2}b\
ight) - \left(1 + \frac{5}{2}b\
ight)$ $4b + \frac{37}{2}$
$(5 + 2b) + \left(2b + \frac{27}{2}\
ight)$ $8b - 15$
$\left(\frac{7}{2}b - 3\
ight) - (8 + 6b)$ $-\frac{5}{2}b - 11$
$(-10 + b) + (7b - 5)$ $-15 - \frac{1}{2}b$

Explanation:

Step1: Simplify first expression

$$\begin{align*} (-14 + \frac{2}{5}b) - (1 + \frac{8}{5}b) &= -14 + \frac{2}{5}b - 1 - \frac{8}{5}b\\ &= (-14-1) + (\frac{2}{5}b - \frac{8}{5}b)\\ &= -15 - \frac{6}{5}b \end{align*}$$

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

$$\begin{align*} (\frac{7}{5}b - 3) - (8 + 6b) &= \frac{7}{5}b - 3 - 8 - 6b\\ &= (\frac{7}{5}b - \frac{30}{5}b) + (-3-8)\\ &= -\frac{23}{5}b - 11 \end{align*}$$

Step4: Simplify fourth expression

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

Answer:

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