Solve the following equation and verify your result:

$5 t$ $-$ 3 = $3 t$ $-$ 5
[2 marks]

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Solution

$5 t$ $-$ 3 = $3 t$ $-$ 5

Transposing the terms, we get
$5 t$ $-$ $3 t$ = $-$ 5 + 3
$\Rightarrow$ $2 t$ = $- 2$
$\Rightarrow$ $t$ = $\frac{- 2}{2}$ = $- 1$
[1 mark]

Let's now verify the result by placing the value of $t$ :
L.H.S. = $5 t$ $-$ 3 = 5( $- 1$ ) $-$ 3 = $-$ 8
R.H.S. = $3 t$ $-$ 5 = 3( $- 1$ ) $-$ 5 = $-$ 8
[1 mark]

Hence, L.H.S. = R.H.S., so verified.

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