[color=#0000ff]Example 1. Solve [math]\large 2x+5=7.[/math][/color][br][br][math] \begin{array}{lrcll}[br]\text{Add -5 to the both sides: } &2x+5&=&7&|-5\\[br] \text{ }&2x+\cancel 5-\cancel 5&=&7-5 \\[br] \text{Divide with a multiplier: }&2x&=&2&|:2\\[br]\text{Give a solution:} &x&=&1&[br]\end{array}[br][/math] [br][br][color=#0000ff]Example 2. Solve [math]\large 3x-5=4x+1.[/math] [/color][br][br][math] \begin{array}{lrcll}[br]\text{Add 5 to the both sides: } & 3x-5&=&4x+1&|+5\\[br]\text{Simplify: }&3x&=&4x+6&|-4x \\[br] \text{Add -4x to the both sides: }&3x-4x&=&4x+6-4x& \\[br]\text{Simplify: }&-x&=&6&|:(-1) \\[br] \text{Divide with a multiplier: }&\dfrac{\cancel{-}x}{\cancel{-1}}&=&\dfrac{6}{-1}&\\[br]\text{Give a solution: } &x&=&-6&[br]\end{array}[br][/math] [br][br][color=#0000ff]Example 3. [/color][br][br][math] \begin{array}{rcll}[br]x-7&=&3x-(6x-8)\\[br]x-7&=&3x-6x+8&|+7\\[br]x&=&-3x+8+7&|+3x\\[br]x+3x&=&15\\[br]4x&=&15&|:4\\[br]x&=&\frac{15}{4}[br]\end{array}[br][/math][br] [br][br][color=#0000ff]Example 4. [/color][br][br][math] \begin{array}{rcll}[br]\frac{4x-2(x-4)}{3}&=&8&|\cdot 3\\[br]4x-2(x-4)&=&24\\[br]4x-2x\textcolor{blue}{+}8&=&24&|-8\\[br]2x&=&16&|:2\\[br]x&=&8[br]\end{array}[/math][br][br] [br] [br][color=#0000ff]Example 5.[/color] [br][br][math]\begin{array}{rcll}[br]\frac{x}{4}-\frac{7x-9}{3}&=&\frac{11}{2}-\frac{x-8}{6}&|\cdot \overbrace{12}^{4\cdot 3}\\[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]\frac{12}{4}x-\frac{12}{3}(7x-9)&=& \frac{12}{2}\cdot 11-\frac{12}{6}(x-8)\\[br]3x-4(7x-9)&=& 6\cdot 11-2(x-8)\\[br]3x-28x\textcolor{blue}{+}36&=&66-2x\textcolor{blue}{+}16&|+2x\\[br]-25x+2x+36&=&82&|-36\\[br]-23x&=&46&|:(-23)\\[br]x&=&-2[br]\end{array}[br][/math][br][br] [br][br][br][br][br][br]