Question
Simplify and solve the linear equation $3(t – 3) = 5(2t + 1).$
✓
Answer
$3 (t – 3) = 5 (2t + 1)$
$ \therefore 3t – 9 = 10t + 5$
$ \therefore 3t – 10t = 5 + 9 ...$ [Transposing $10t$ to $L.H.S$. and $–9$ to $R.H.S.]$
$ \therefore –7t = 14$
$ \therefore t = -\frac{{14}}{7} ...$ [Dividing both sides by $–7]$
$ \therefore t = –2$
this is the required solution.
Verification,
$L.H.S. = 3(t – 3) = 3(–2 – 3) = 3(–5) = –15$
$R.H.S. = 5(2t + 1) = 5(2 \times (–2) + 1) = 5(– 4 + 1)$
$= 5(–3) = –15 = L.H.S$
$ \therefore 3t – 9 = 10t + 5$
$ \therefore 3t – 10t = 5 + 9 ...$ [Transposing $10t$ to $L.H.S$. and $–9$ to $R.H.S.]$
$ \therefore –7t = 14$
$ \therefore t = -\frac{{14}}{7} ...$ [Dividing both sides by $–7]$
$ \therefore t = –2$
this is the required solution.
Verification,
$L.H.S. = 3(t – 3) = 3(–2 – 3) = 3(–5) = –15$
$R.H.S. = 5(2t + 1) = 5(2 \times (–2) + 1) = 5(– 4 + 1)$
$= 5(–3) = –15 = L.H.S$
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