Question
Solve the following equation and verify the answer: $3(x + 6) + 2(x + 3) = 64$
✓
Answer
$3(x + 6) + 2 (x + 3) = 64 $
$\Rightarrow 3x + 18 + 2x + 6 = 64$ (Removing brackets)
$\Rightarrow 3x + 2x + 18 + 6 = 64 $
$\Rightarrow 5x + 24 = 64 $
$\Rightarrow 5x = 64 - 24$ (Transposing $24$ to $R.H.S.) $
$\Rightarrow 5x = 40$
$\Rightarrow\frac{\text{5x}}{5}=\frac{40}{5}$(Dividing both sides by $5)$
$\Rightarrow x = 8$
So, $x = 8$ is a solution of the given equation.
Check: Substituting $x = 8$ in the given equation,
we get $L.H.S. = 3(8 + 6) + 2(8 + 3) = 3 \times 14 + 2 \times 11 = 42 + 22 = 64 = R.H.S.$
$\therefore$ When $x = 8$, we have $L.H.S. = R.H.S$
$\Rightarrow 3x + 18 + 2x + 6 = 64$ (Removing brackets)
$\Rightarrow 3x + 2x + 18 + 6 = 64 $
$\Rightarrow 5x + 24 = 64 $
$\Rightarrow 5x = 64 - 24$ (Transposing $24$ to $R.H.S.) $
$\Rightarrow 5x = 40$
$\Rightarrow\frac{\text{5x}}{5}=\frac{40}{5}$(Dividing both sides by $5)$
$\Rightarrow x = 8$
So, $x = 8$ is a solution of the given equation.
Check: Substituting $x = 8$ in the given equation,
we get $L.H.S. = 3(8 + 6) + 2(8 + 3) = 3 \times 14 + 2 \times 11 = 42 + 22 = 64 = R.H.S.$
$\therefore$ When $x = 8$, we have $L.H.S. = R.H.S$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Arrange the following numbers in ascending order: $1020304, 893245, 980134, 1021403, 893425, 1020216$
→Name the points and then the line segments in each of the following figures:
The perimeter of a square garden is $48m.$ A small flower bed covers $18\ sq-m$ area inside this garden. What is the area of the garden that is not covered by the flower bed? What fractional part of the garden is covered by flower bed? Find the ratio of the area covered by the flower bed and the remaining area.
→Using a pair of compasses construct the following angles: $60^\circ $
→Arrange the fractions $\frac67,\frac78,\frac45$ and $\frac34$ in descending order.
→What is the area of each small square in the Fig. if the area of entire figure is $96\ sq-cm$. Find the perimeter of the figure.
→Arrange the following numbers in descending order: $5032786, 23794206, 5032790, 23756819, 987876$
→Draw an angle of measure $153^\circ $ and divide it into four equal parts.
→Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?
The ratio of male and female employees in a multinational company is $5 : 3.$ If there are $115$ male employees in the company, then the number of female employees is:
→