I need help with my algebra homework?! can you please help me?!

Question

1) Determine whether the given value makes a true statement 3b-5 < 2b+7 when B=6

2)Name the common factors of the terms.
12x3, 18x2, and 9x

3) Prove that 7*(1-m)*2= 14-14m. Prove the statement algebraically, and just simplify each step with a definition, property or previously proven statement.

Answer 1

3.

Solve the left hand side equation = 7*(1-m)*2.

Apply distributive property: a(b+c) =  ab+ac

= (7*1+7*-m)*2

= (7+7*-m)*2               

= (7-7m)*2       

Apply distributive property: (b-c)a =  ba-ca

= 7*2-7m*2

=14-14m.

Answer 2

3b-5 < 2b+7 when B=6

Substitute b=6 in above statement

3 (6) - 5 < 2 (6) + 7

18 - 5 < 12 + 7                 (Multiply: 3(6) = 18; Multiply: 2(6) = 12)

13 < 19

The given statement is true

Answer 3

2) 12x3, 18x2, and 9x

Write the prime factorization of each  monomial.

12x3 = 2 × 2 × 3 × x  × x × x

18x2 = 2 × 3 × 3 × x  × x

9x  = 3 × 3 × x

The product of the common prime factors in each monomial = 3 × x  = 3x

The common factor of 12x3 , 18x2 and 9x is 3x.