Algebra help please!?

Question

-7r - 8 = -5r + 3

0.3(p + 4) = 2.7p

4q + 19 = 5/6q

If you can just walk me through the steps for each problem, I'd really appreciate ti! My aglebra teacher always manages to confuse me more and I do not understand what I'm suppose to do. Thank you so much in advance!

Answer 1

Remember that you need to isolate your variable and that anything you do to one side of the equation needs to be done to the other side, as well.

First problem:
-7r - 8 = -5r + 3

Add 5r to both sides to nullify the -5r on the right:
-7r - 8 + 5r = -5r + 3 + 5r

Also, add 8 to both sides to nullify the -8 on the left. This leaves only the r terms on the left:
-7r - 8 + 5r + 8 = -5r + 3 + 5r + 8
-2r = 11

Divide both sides by -2 to get r all by itself:
-2r / (-2) = 11 / (-2)
r = -11/2

Second problem:
Distribute through. Multiply everything out so you can isolate p.
0.3(p + 4) = 2.7p
0.3p + 4(0.3) = 2.7p
0.3p + 1.2 - 0.3p = 2.7p - 0.3p (I combined two steps here by subtracting 0.3p from both sides).
1.2 = 2.4p
1.2 / 2.4 = 2.4p / 2.4
p = 0.5

Third problem:
I'm assuming you mean (5/6)q, which means the q is in the numerator. The way you have it written, it could mean 5/(6q). If you mean that, let us know. For now, I'll assume (5/6)q.

I'll do something a little different here. Fractions can be a pain to work with, so I'll get rid of them. I'll multiply the entire equation by 6.

4q + 19 = 5/6q
6(4q + 19) = 6(5/6q)
24q + 114 = 5q
24q - 5q + 114 - 114 = 5q - 5q - 114
19q = -114
19q / 19 = -114 / 19
q = -6

Hope that helps you with the rest of your assignment.

Answer 2

Perform the same operation (add, subtract, multiply or divide) on both sides of the equation to get the form

variable = number

-7r - 8 = -5r + 3

-7r - 8 +5r = -5r + 3 + 5r {add 5r}
-2r - 8 = 3 {collect like terms}
-2r - 8 + 8 = 3 + 8 {add 8}
-2r = 11 (collect like terms}
-2r/(-2) = 11/(-2) {divide by -2}
r = -11/2

0.3(p + 4) = 2.7p
0.3p + 1.2 = 2.7p (distribute .3 over p and 4}
0.3p + 1.2 - 2.7p - 1.2 = 2.7p - 2.7p - 1.2 {subtract 2.7p, 1.2}
-2.4p = - 1.2 {collect like terms}
p = 1/2 (divide by 2.4}


4q + 19 = 5/6q

I guess you mean

4q + 19 = 5q/6

When there are fractions in the equation, you can clear them by multiplying both sides by their LCD. Here there is only one fraction

6(4q + 19) = 6(5q/6)
24q + 114 = 5q (distribute & simplify}
19q = - 114 {subtract 5q, 114}
q = - 6 {divide by 19}

Be careful, follow the rules, watch to get the signs right.

Answer 3

-7r - 8 = -5r + 3 add 5r to both sides
-7r +5r - 8 = -5r + 5r + 3
-2r -8 = 3 add 8 to both sides
-2r -8 + 8 = 3 + 8
-2r = 11 divide by 2
r = -[11/2]

0.3(p+4) = 2.7p
0.3p + 1.2 = 2.7p
3p = 1.2
p = 0.4

4q + 19 = [5/6]q
[24/6]q + [114/6] = [5/6]q
[19/6]q = -[114/6]
q = -[114/6] * [6/19]
q = -6

Answer 4

1. -7r-8=-5r+3
add -7 to -5 -8=2r+3
subtract 3 -11=2r
divide by 2 -11/2=r

2. .3(p+4)=2.7p
simplify .3p+1.2=2.7p
subtract .3 1.2=2.4p
divide by 2.4 .5=p

3. 4q+19=5/6q
subtract 4q 19=-3 1/6q
divide by -3 1/6 6~q (q is about 6)

Answer 5

i will solve one for you and rest you can follow.

take second problem:
0.3(p + 4) = 2.7p
open the bracket
0.3p +0.3*4 =2.7p
0.3p + 1.2 = 2.7p
subtract 2.7p from both sides:
0.3p-2.7p +1.2 =0
-2.4p +1.2 =0
subtract 1.2 from both sides:
-2.4p = -1.2
multiply both sides by -1:
2.4p = 1.2
divide both sides by 2.4
p = 1.2/2.4
multiply numerator and denominator by 10 each
p = 12/24
or p = 1/2

similarly solve for other equations also.

Answer 6

-7r-8=-5r+3
-7r+5r=3+8
-2r=11
r=-11/2
r=5.5

0.3(p+4)=2.7p
0.3p+1.2=2.7p
2.7p-0.3p=1.2
2.4p=1.2
p=0.5

4q+19=5/6q
4q-5/6q=-19
4q-0.83q=-19
3.17q=-19
q=5.99
q=6.00