Solve the algebra equation- unsure about order of operations, how to go about solving, solve for x The question states: solve the equation. State the solution set and check your answer.
I've spent a good 45 minutes on this, to know avail. If someone could sort of walk me through this I would be appreciative. I don't just want an answer I would really like to understand it. Thank you
$$\frac{0.12(a+2)}{3}= 0.114$$
 A: $$\frac{0.12(a+2)}{3}= 0.114 \overset{(1)}{\iff} (a+2)=\frac{0.12(a+2)}{3}\cdot \frac{3}{0.12}= 0.114 \cdot \frac{3}{0.12} \\ \overset{(2)}{\iff} a=(a+2)-2 = 0.114 \cdot \frac{3}{0.12}-2 = 0.85$$
(1) Multiply both sides of the equation by $\frac{3}{0.12}$
(2) Add $-2$ to both sides of the equation
A: Here are some ideas. One thing to get sorted out is the order in which to do things. Here, for example, you can see that $\cfrac {0.12}3=0.04$. This is the easiest way to get rid of that awkward looking $3$.
So then you have $0.04(a+2)=0.114$
Now you might not like dividing decimals, so you can multiply both sides by $1000$ [$500$ would do, but lets keep the arithmetic easy to avoid errors]
This gives $40(a+2)=114$
Now clear the bracket which gives $40a+80=114$, subtract $80$ from each side to give $40a=34$ and then divide both sides by $40$ to give $a=\cfrac {17}{20} (=0.85)$
The factor $2$ which cancelled at the end came from multiplying by $1000$ rather than $500$ earlier on.
This is not the quickest way to proceed - especially if you have a calculator to hand - but the principle of doing easy simplifications first means that each step is straightforward.
