Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6
EXERCISE 2.3
Question 1 :
Solve and check result : 3x = 2x + 18
Sol :
3x = 2x + 18
On transposing 2x to L.H.S , we obtain
3x – 2x = 18
x = 18
L.H.S \( \begin{align*}&=3x\\&=3\times{}18\\&=54\end{align*} \)
R.H.S \( \begin{align*}&=2x+18\\&=2\times{18}+18\\&=36+18\\&=54\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 2 :
Solve and check result :
5t – 3 = 3t – 5
Sol :
5t – 3 = 3t – 5
On transposing 3t to L.H.S and -3 to R.H.S , we obtain
5t – 3t = -5 – (-3)
2t = -2
On dividing both sides by 2 , we obtain
t = -1
L.H.S \( \begin{align*}\end{align*} \)
R.H.S \( \begin{align*}\end{align*} \)
L.H.S = R.H.S
Question 3 :
Solve and check result :
5x +9 = 5 + 3x
Sol :
On transposing 3x to L.H.S and 9 to R.H.S , we obtain
5x – 3x = 5 – 9
2x = -4
On dividing both sides by 2 , we obtain
x = -2
L.H.S \( \begin{align*}&=5x+9\\&=5\times(-2)+9\\&=-10+9\\&=-1\end{align*} \)
R.H.S \( \begin{align*}&=5+3\times(-2)\\&=5-6\\&=-1\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 4 :
Solve and check result :
4z + 3 = 6 +2z
Sol :
4z + 3 = 6 +2z
On transposing 2z to L.H.S and 3 to R.H.S , we obtain
4z – 2z = 6 – 3
2z = 3
Dividing both sides by 2 , we obtain
\( z=\dfrac{3}{2} \)
L.H.S \( \begin{align*}&=4z+3\\&=4\times{\dfrac{3}{2}}+3\\&=6+3\\&=9\end{align*} \)
R.H.S \( \begin{align*}&=6+2z\\&=6+2\times\dfrac{3}{2}\\&=6+3\\&=9\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 5 :
Solve and check result :
2x – 1 = 14 – x
Sol :
2x – 1 = 14 – x
Transposing x to L.H.S and 1 to R.H.S , we obtain
2x + x = 14 + 1
3x = 15
Dividing both sides by 3 , we obtain
x = 5
L.H.S \( \begin{align*}&=2x-1\\&=2\times(5)-1\\&=10-1\\&=9\end{align*} \)
R.H.S \( \begin{align*}&=14-x\\&=14-5\\&=9\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 6 :
Solve and check result :
8x + 4 = 3(x – 1)+ 7
Sol :
8x + 4 = 3(x – 1)+ 7
8x + 4 = 3x – 3 + 7
On transposing 3x to L.H.S and 4 to R.H.S , we obtain
8x – 3x = – 3 + 7 – 4
5x = – 7 + 7
x = 0
L.H.S \( \begin{align*}&=8x+4\\&=8\times(0)+4\\&=4\end{align*} \)
R.H.S \( \begin{align*}&=3(x-1)+7\\&=3(0-1)+7\\&=-3+7\\&=4\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 7 :
Solve and check result :
\( x=\dfrac{4}{5}(x+10) \)
Sol :
\( x=\dfrac{4}{5}(x+10) \)
Multiply both sides by 5 , we obtain
5x = 4(x + 10)
5x = 4x + 40
On transposing 4x to L.H.S , we obtain
5x – 4x = 40
x = 40
L.H.S = x = 40
R.H.S \( \begin{align*}&=\dfrac{4}{5}(x+10)\\&=\dfrac{4}{5}(40+10)\\&=\dfrac{4}{5}\times{50}\\&=40\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 8 :
Solve and check result :
\( \dfrac{2x}{3}+1=\dfrac{7x}{15}+3 \)
Sol :
\( \dfrac{2x}{3}+1=\dfrac{7x}{15}+3 \)
On transposing \( \dfrac{7x}{15} \) to L.H.S and 1 to R.H.S , we obtain
\( \dfrac{2x}{3}-\dfrac{7x}{15}=3-1 \)
\( \dfrac{5\times2x-7x}{15}=2 \)
\( \dfrac{3x}{15}=2 \)
Multiplying both sides by 5 , we obtain
x = 10
L.H.S \( \begin{align*}&=\dfrac{2x}{3}+1\\&=\dfrac{2\times{10}}{3}+1\\&=\dfrac{2\times{10}+1\times3}{3}\\&=\dfrac{23}{3}\end{align*} \)
R.H.S \( \begin{align*}&=\dfrac{7x}{15}+3\\&=\dfrac{7\times10}{15}+3\\&=\dfrac{7\times2}{3}+3\\&=\dfrac{14}{3}+3\\&=\dfrac{14+3\times3}{3}\\&=\dfrac{23}{3}\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 9 :
Solve and check result :
\( 2y+\dfrac{5}{3}=\dfrac{26}{3}-y \)
Sol :
\( 2y+\dfrac{5}{3}=\dfrac{26}{3}-y \)
On transposing y to L.H.S and \( \dfrac{5}{3} \) to R.H.S , we obtain
\( 2y+y=\dfrac{26}{3}-\dfrac{5}{3} \)
\( 3y=\dfrac{21}{3}=7 \)
Dividing both sides by 3 , we obtain
\( y=\dfrac{7}{3} \)
L.H.S \( \begin{align*}&=2y+\dfrac{5}{3}\\&=2\times\dfrac{7}{3}+\dfrac{5}{3}\\&=\dfrac{14}{3}+\dfrac{5}{3}\\&=\dfrac{19}{3}\end{align*} \)
R.H.S \( \begin{align*}&=\dfrac{26}{3}-y\\&=\dfrac{26}{3}-\dfrac{7}{3}\\&=\dfrac{19}{3}\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
Question 10 :
Solve and check result :
\( 3m=5m-\dfrac{8}{5} \)
Sol :
\( 3m=5m-\dfrac{8}{5} \)
On transposing 5m to L.H.S , we obtain
\( 3m-5m=-\dfrac{8}{5} \)
\( -2m=-\dfrac{8}{5} \)
Dividing both sides by -2 , we obtain
\( m =\dfrac{4}{5} \)
L.H.S \( \begin{align*}&=3m\\&=3\times\dfrac{4}{5}\\&=\dfrac{12}{5}\end{align*} \)
R.H.S \( \begin{align*}&=5m-\dfrac{8}{5}\\&=5\times\dfrac{4}{5}-\dfrac{8}{5}\\&=\dfrac{12}{5}\end{align*} \)
L.H.S = R.H.S
Hence, the result obtained above is correct
