[math]\Large\begin{eqnarray}[br]x-7&=&3x-(6x+8)\\[br]x-7&=&3x-6x\textcolor{red}{-} 8\\[br]x-7&=&-3x-8&|+3x\\[br]x-7+3x&=&-8&|+7\\[br]4x&=&-8+7\\[br]4x&=&-1&|:4\\[br]x&=&-\frac{1}{4}[br]\end{eqnarray}[br][/math]

 [math]\Large\begin{eqnarray}[br]\frac{4x-2(x-4)}{3}&=&8&|\cdot 3\\[br]4x-2(x-4)&=&24\\[br]4x-2x\textcolor{red}{+}8&=&24&|-8\\[br]2x&=&16&|:2\\[br]x&=&8[br]\end{eqnarray}[/math]

 [math]\Large\begin{eqnarray}[br]\frac{x}{4}-\frac{7x-9}{3}&=&\frac{11}{2}-\frac{x-8}{6}&|\cdot 12\\[br]12\cdot\left [ \frac{x}{4}-\frac{7x-9}{3}\right ]&=&12\cdot \left [\frac{11}{2}-\frac{x-8}{6}\right ]\\[br]12\cdot\frac{x}{4}-12\cdot\frac{7x-9}{3}&=&12\cdot\frac{11}{2}-12\cdot\frac{x-8}{6}\\[br]3x-4\cdot(7x-9)&=&6\cdot 11-2\cdot (x-8)\\[br]3x-4\cdot 7x\textcolor{red}{+}36&=&66-2x\textcolor{red}{+}16\\[br]3x-28x\textcolor{blue}{+}2x&=&66+16\textcolor{blue}{-}36\\[br]-23x&=&46\\[br]x&=&-2[br][br]\end{eqnarray}[/math]

The price of a product was raised by 16% and the new increased price was 754 euros. What was the price before the raise?[br][br]The original price is unknown, so let us mark it with [i]x[/i].  That price was raised by 16%, so the raise in euros is [math]\Large 0.16x[/math]. [br][br]The new price is the original price plus the raise, so[br][br][math]\LARGE\begin{eqnarray} x+0.16x&=&754\text{ euros}\\[br]1.16x&=&754\text{ euros}\\[br]x&=&650\text{ euros}\end{eqnarray}[/math][br][br]The price before the raise was 650 euros.

A carpet is in sale. The price of the carpet is 39 euros and it is said that price is decreased by 43%. What was the original price of this carpet?[br][br]The original price is unknown, so let us mark it with [i]x[/i].  That price was decreased by 43%, so the decrease in euros is [math]\Large 0.43x[/math]. [br][br]The new price is the original price minus the decrease, so[br][br][math]\LARGE\begin{eqnarray} x-0.43x&=&39\text{ euros}\\[br]0.57x&=&39\text{ euros}\\[br]x&=&68.42\text{ euros}\end{eqnarray}[/math][br][br]The price before the decrease was about 68 euros.

You paid 35 € for a hair cut. How much of it stays at hairdresser's?[br][br][br]The price with VAT consists of the [i]price without VAT + VAT.[/i] As the price without VAT is unknown, we can mark it with [i]x[/i]. VAT in Finland for hairdresser's services is 24%. Thus,[br][br][math]\Large \begin{eqnarray}x+0.24x&=&35\text{ euros}&\\[br]1.24x&=&35\text{ euros}&|\text{banana+half of banana=(1+0.5) banana}\\[br]x&\approx &28.22\text{ euros}&[br]\end{eqnarray}[/math]

You have noticed that you need 1500 euros for living in a month. Your Finnish personal scale of taxation says, that you have to pay 15% tax till 900 euros and, after that, 27%. How much should your monthly salary be so that you earn 1500 euros at least?[br][br]Your monthly salary is unknown [i]x[/i]. As you must earn more than 900 euros, you have to pay 27% of [u]part exceeding 900 euros[/u]. Thus, your net salary is[br][br][math]\LARGE \begin{eqnarray}[br]x-0.15x-0.27(x-900)&=&1500\\[br]x-0.15x-0.27x\textcolor{blue}{+}243&=&1500\\[br]0.58x+243&=&1500\;\;\;\;\;\;\;\;\;\;\;\;|-243\\[br]0.58x&=&1500-243\\[br]0.58x&=&1257\;\;\;\;\;\;\;\;\;\;\;\;|:\,0.58\\[br]x&=&2167.24[br]\end{eqnarray}[/math][br][br]So, you should earn about 2170 euros per month.