Connect with a community of experts and enthusiasts on IDNLearn.com. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.

Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.

A. \(\left(-14+\frac{3}{2} b\right)-\left(1+\frac{8}{2} b\right)\)

B. \(4b + \frac{13}{2}\)

C. \((5+2b) + \left(2b+\frac{3}{2}\right)\)

D. \(8b - 15\)

E. \(\left(\frac{7}{2}b - 3\right) - (8 + 6b)\)

F. \(\frac{-5}{2}b - 11\)

G. \((-10 + b) + (7b - 5)\)

H. [tex]\(-15 - \frac{5}{2}b\)[/tex]


Sagot :

Okay, let's match the pairs of equivalent expressions step-by-step:

1. Expression: \((-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)\)
- Simplify the expression:
[tex]\[ (-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b) \][/tex]
[tex]\[ = -14 + \frac{3}{2} b - 1 - 4 b \][/tex]
[tex]\[ = -15 + \left(\frac{3}{2} - 4\right)b \][/tex]
[tex]\[ = -15 - \frac{5}{2} b \][/tex]
- Hence, the pair is: \((-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)\) and \(-15 - \frac{5}{2} b\).

2. Expression: \((5 + 2 b) + (2 b + \frac{3}{2})\)
- Simplify the expression:
[tex]\[ (5 + 2 b) + (2 b + \frac{3}{2}) \][/tex]
[tex]\[ = 5 + 2b + 2b + \frac{3}{2} \][/tex]
[tex]\[ = 5 + \frac{3}{2} + 4b \][/tex]
[tex]\[ = \frac{10}{2} + \frac{3}{2} + 4b \][/tex]
[tex]\[ = \frac{13}{2} + 4b \][/tex]
- Hence, the pair is: \((5 + 2 b) + (2 b + \frac{3}{2})\) and \(4 b + \frac{13}{2}\).

3. Expression: \(\left(\frac{7}{2} b - 3\right) - (8 + 6 b)\)
- Simplify the expression:
[tex]\[ \left(\frac{7}{2} b - 3\right) - (8 + 6 b) \][/tex]
[tex]\[ = \frac{7}{2} b - 3 - 8 - 6 b \][/tex]
[tex]\[ = -3 - 8 + \left(\frac{7}{2} - 6\right) b \][/tex]
[tex]\[ = -11 - \frac{5}{2} b \][/tex]
- Hence, the pair is: \((\frac{7}{2} b - 3) - (8 + 6 b)\) and \(-11 - \frac{5}{2} b\).

4. Expression: \((-10 + b) + (7 b - 5)\)
- Simplify the expression:
[tex]\[ (-10 + b) + (7 b - 5) \][/tex]
[tex]\[ = -10 + b + 7b - 5 \][/tex]
[tex]\[ = -10 - 5 + 8b \][/tex]
[tex]\[ = -15 + 8b \][/tex]
- Hence, the pair is: \((-10 + b) + (7 b - 5)\) and \(8 b - 15\).

Therefore, the correct pairs are:
1. \((-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)\) and \(-15 - \frac{5}{2} b\).
2. \((5 + 2 b) + (2 b + \frac{3}{2})\) and \(4 b + \frac{13}{2}\).
3. \((\frac{7}{2} b - 3) - (8 + 6 b)\) and \(-11 - \frac{5}{2} b\).
4. [tex]\((-10 + b) + (7 b - 5)\)[/tex] and [tex]\(8 b - 15\)[/tex].