Find the value:
1. 7x - 5 = 2x
2. 5x - 12 = 2x - 6
3. 7p - 3 = 3p + 8

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Solution

1. $7 x - 5 = 2 x$

$\Rightarrow 7 x - 5 - 2 x = 2 x - 2 x$

$\Rightarrow 7 x - 2 x - 5 = 0$

$\Rightarrow 5 x - 5 = 0$

$\Rightarrow 5 x - 5 + 5 = 0 + 5$

$\Rightarrow 5 x = 5$

$\Rightarrow \frac{5 x}{5} = \frac{5}{5}$

$x = 1$

$\Rightarrow x = 1$

2. $5 x - 12 = 2 x - 6$

$\Rightarrow 5 x - 12 - 2 x = 2 x - 6 - 2 x$

$\Rightarrow 5 x - 2 x - 12 = 2 x - 2 x - 6$

$\Rightarrow 3 x - 12 = 0 - 6$

$\Rightarrow 3 x - 12 + 12 = - 6 + 12$

$\Rightarrow 3 x = 6$

$x = 2$

$\Rightarrow x = 2$

3. $7 p - 3 = 3 p + 8$

$\Rightarrow 7 p - 3 - 3 p = 3 p + 8 - 3 p$

$\Rightarrow 7 p - 3 p - 3 = 3 p - 3 p + 8$

$\Rightarrow 4 p - 3 = 8$

$\Rightarrow 4 p - 3 + 3 = 8 + 3$

$p = \frac{11}{4}$

$\Rightarrow 4 p = 11 \Rightarrow p = \frac{11}{4}$

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