Solve the following equations without transposing and check your result:
$5 y + 10 = 4 y - 10$ .

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Solution

Here, we put different values of $y$ in the given equation $5 y + 10 = 4 y - 10$ .

When $x = 5$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (5) + 10 = 4 (5) - 10$

$⟹$ $35 \neq 10$ .

When $x = - 5$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (- 5) + 10 = 4 (- 5) - 10$

$⟹$ $- 15 \neq - 30$ .

When $x = 10$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (10) + 10 = 4 (10) - 10$

$⟹$ $60 \neq 30$ .

When $x = - 10$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (- 10) + 10 = 4 (- 10) - 10$

$⟹$ $- 40 \neq - 50$ .

When $x = 15$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (15) + 10 = 4 (15) - 10$

$⟹$ $85 \neq 50$ .

When $x = - 15$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (- 15) + 10 = 4 (- 15) - 10$

$⟹$ $- 65 \neq - 70$ .

When $x = 20$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (20) + 10 = 4 (20) - 10$

$⟹$ $110 \neq 70$ .

When $x = - 20$ ,
$5 y + 10 = 4 y - 10 ⟹$ $5 (- 20) + 10 = 4 (- 20) - 10$

$⟹$ $- 90 = - 90$ .

Therefore, the value of $y$ is $- 20$ .

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3 x + 4 = 19

5 x - 3 = 3 x + 5

3 (y - 1) = y + 1

x = \frac{4}{5} (x + 10)

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