Explore a diverse range of topics and get expert answers on IDNLearn.com. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

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].