math question, solve for...?

Question

ok here is an easy algebra question( for some)

1(a+3)+2=4(a+5)+6
very simple, solved in steps...

step1:1(a+3)+2=4(a+5)+6
step2:1a+4+2=4a+9+6
step3:1a+4+2-1a=4a+9+6-1a
step4:4+2=3a+9+6
step5:4+2-2=3a+9+6-2
step6:4=3a+9+4
step7:4-4=3a+9+4-4
step8:0=3a+9
step9:0-9=3a+9-9
step10:-10=3a
step11:-10/3=3a/3
step12:a=3.33( im just going out to hundreth decimal, dosent really matter since 3.33 represents 3.3333333.... or 3.33 repeating )

its a very simple proccess
that was a problem with low numbers

the challenge is to solve this:
21(a+9)=13(a+8)+1
what does "a" equal?

p.s. rscanner

i was taught not to move the variables at all
also u dont have to explain , eather you know it or you dont

also, rscanner i dont know u personnaly, but from reading your post , i would guess ur an uptight air-head
>=D

Answer 1

21(a+9)=13(a+8)+1
21a+189=13a+104+1
21a+189=13a+105
8a+189=105
8a= -84
a= -10.5

Answer 2

You are doing this the hard way.

First expand the parenthesis

21a + 189 = 13a + 104 + 1

move all "a" terms to the left side and all constant terms to the right side

21a - 13a = -189 + 104 + 1

combine terms

8a = -84

divide both sides by 8 to remove the multiplier on "a"

a = -84/8 = -21/2 = -10 1/2

not so many steps as your first problem - you are confusing yourself.


Also in the first problem you expanded the parenthesis incorrectly
You are adding rather than multiplying using the distributive propertly

Step 2 should be
a+3+2=4a+20+6

so now everything is wrong from there on.

Answer 3

You use the exact same process:

21(a + 9) = 13(a + 8) + 1 --- Distribute the 21 and 13...
21a + 189 = 13a + 104 + 1 --- Combine like terms, and subtract 13a from each side...
8a + 189 = 105 --- Subtract 189 from both sides...
8a = (-84) --- Divide both sides by 8...
a = 10½ or 10.5

Answer 4

21(a+9)=13(a+8)+1
-use the distributive property and you get the answer below
21a+189=13a+104+1
-then subtract 13a from 21a because 13a is being added to 104, you do da opposite
8a+189=101+1
-then you combine 101 and 1 to get 102
8a+189=102
-subtract 189 from 102 because you do da opposite of what is begin done to da number.
8a=(-87)
-then you divide by the number with da variable which is 8a
8a/8a=(-87)/8a
-your answer is a=(-10.875)
its a negitave because a negitave divided by a positive is negitive, and these equations dont always have to come out evenly.

Answer 5

21(a+9)=13(a+8)+1

21a+189=13a+105

8a= -84

a= -10.5

Answer 6

21a + 189 = 13a + 104 + 1
8a + 189 = 105
8a = -84
a = -10.5

Answer 7

I can never figer this out.

Answer 8

you have too much free time.