Algebra solutions

1. Find the LCM of 20 and 44.

Ans. The prime factorization of 44 is,
44=2×2×11
The prime factorization of 20 is,
20=2×2×5
The LCM of 20 and 44 is,
2×2×5×11=220

2. Divide and simplify the following: 24/22÷16/55

Ans. 24/22÷16/55=(24⁄22)/(16/55)=24/22×55/16=6/2×5/4=30/8=15/4=3.75

Simplify the following: 7/15-6/5+9/10
Ans.
7/15-6/5+9/10=(14-36+27)/30=5/30=1/6=0.167

3. Solve for w: w/4+w/3=28
Ans.

w/4+w/3=28
(3w+4w)/12=28
7w/12=28
7w=28×12→7w=336→w=336/7→w=48

4. Solve the following for x: -6x+5.4=63+1.2x
Ans. Rearrange the equation,
-6x-1.2x =63-5.4

-7.2x=57.6→x=-57.6/7.2→x=-8

6. Simplify the following, combining like terms: 2a – 4(a + b) – (a – 2b)
Ans.
2a – 4a-4 b – a+ 2b=-3a-2b→-3a=2b→a-2/3 b