Ex.4.1 Q1 Simple-Equations Solution - NCERT Maths Class 7

Go back to  'Ex.4.1'

Question

Complete the last column of the table.

S. No

Equation

Value

Say, whether the equation
is satisfied. (Yes/No)

(i)

\(x + 3 = 0\)

\(x= 3\)

 

(ii)

\(x + 3 = 0\)

\(x= 0\)

 

(iii)

\(x + 3 = 0\)

\(x= -3\)

 

(iv)

\(x - 7 = 1\)

\(x= 7\)

 

(v)

\(x - 7 = 1\)

\(x= 8\)

 

(vi)

\(5x= 25\)

\(x= 0\)

 

(vii)

\(5x= 25\)

\(x= 5\)

 

(viii)

\(5x= 25\)

\(x= -5\)

 

(ix)

\(\begin{align}\frac{m}{3} = 2\end{align}\)

\(m= -6\)

 

(x)

\(\begin{align}\frac{m}{3} = 2\end{align}\)

\(m= 0\)

 

(xi)

\(\begin{align}\frac{m}{3} = 2\end{align}\)

\(m= 6\)

 

Text Solution

What is Known?

Equation and the value of the variable.

What is unknown?

Whether the given value is a solution of the equation or not.

Reasoning:

Put the value of the variable in the given equation. If LHS is equal to the RHS then the equation is satisfied and if it is not that means this given value is not a solution of the equation.

Steps:

(i) \(\begin{align}x + 3 = 0,x = 3\end{align}\)

L.H.S \(=\) \(x+ 3\), R.H.S \(= 0\)

By putting, \(x= 3\)

L.H.S \( =3 + 3= 6 ≠ \)R.H.S

Therefore, “No”, the equation is not satisfied.

(ii) \(\begin{align}x+ 3 = 0,x= 0\end{align}\)

L.H.S \(=\) \(x+ 3\), R.H.S\(= 0\)

By putting, \(x= 0;\)

L.H.S \( =0+3= 3 ≠\)R.H.S

Therefore, “No”, the equation is not satisfied.

(iii) \(\begin{align}x+ 3 = 0, x= -3\end{align}\)

L.H.S \(=\) \(x+ 3\), R.H.S \(= 0\)

By putting, \(x= -3\)

L.H.S \(= -3 + 3 = 0 =\) R.H.S

Therefore, “Yes”, the equation is satisfied.

(iv) \(\begin{align}x– 7 = 1, x= 7\end{align}\)

L.H.S \(=\) \(x\,– 7\), R.H.S \(= 1\)

By putting, \(x= 7\);

L.H.S \(= 7 \,– 7 = 0 ≠\) R.H.S

Therefore, “No”, the equation is not satisfied.

(v) \(\begin{align}x– 7 = 1, x= 8\end{align}\)

L.H.S \(=\) \(x– 7\), R.H.S \(= 1\)

By putting, \(x= 8;\)

L.H.S \(= 8 \,– 7 = 1 =\) R.H.S

Therefore, “Yes”, the equation is satisfied.

(vi) \(\begin{align}5x= 25, x= 0,\end{align}\)

L.H.S \(=\) \(5x\), R.H.S\( = 25\)

By putting, \(x= 0;\)

L.H.S \(=\) \(5 \times 0=0 ≠ \)R.H.S

Therefore, “No”, the equation is not satisfied.

(vii) \(\begin{align}5x= 25, x= 5,\end{align}\)

L.H.S \(= 5x\), R.H.S \(= 25\)

By putting, \(x= 5;\)

L.H.S \(=\) \(5 \times 5 = 25\)= R.H.S

Therefore, “Yes”, the equation is satisfied.

(viii) \(\begin{align}5x = 25, x= – 5,\end{align}\)

L.H.S \(=\) \(5x\), R.H.S \(= 25\)

By putting, \(x= – 5;\)

L.H.S \(=\) \(5 \times \left( { - 5} \right) = - 25≠\)R.H.S

Therefore, “No”, the equation is not satisfied.

(ix) \(\begin{align}\frac{m}{3} = 2, m= – 6,\end{align}\)

L.H.S \(=\) \(\begin{align}\frac{m}{3}\end{align}\), R.H.S \(= 2\)

By putting, \(m\)\(= – 6;\)

L.H.S \(=\) \(\begin{align}\frac{{ - 6}}{3}=−2≠\end{align}\) R.H.S

Therefore, “No”, the equation is not satisfied.

(x) \(\begin{align}\frac{m}{3} = 2, m=0\end{align}\)

L.H.S \(=\) \(\begin{align}\frac{m}{3}\end{align}\), R.H.S \(= 2\)

By putting, \(m= 0;\)

L.H.S \(=\) \(\begin{align}\frac{0}{3}=0≠\end{align}\)R.H.S

Therefore, “No”, the equation is not satisfied.

(xi) \(\begin{align}\frac{m}{3} = 2 m= 6,\end{align}\)

L.H.S \(=\) \(\begin{align}\frac{m}{3}\end{align}\), R.H.S \(= 2\)

By putting, \(m\) \(= 6;\)

L.H.S \(=\) \(\begin{align}\frac{6}{3}= 2 =\end{align}\) R.H.S

Therefore, “Yes”, the equation is satisfied

S. No

Equation

Value

Say, weather the equation is satisfied. (Yes/No)

(i)

\(x + 3 = 0\)

\(x= 3\)

No

(ii)

\(x + 3 = 0\)

\(x= 0\)

No

(iii)

\(x + 3 = 0\)

\(x= -3\)

Yes

(iv)

\(x - 7 = 1\)

\(x= 7\)

No

(v)

\(x - 7 = 1\)

\(x= 8\)

Yes

(vi)

\(5x= 25\)

\(x= 0\)

No

(vii)

\(5x= 25\)

\(x= 5\)

Yes

(viii)

\(5x= 25\)

\(x= -5\)

No

(ix)

\(\begin{align}\frac{m}{3} = 2\end{align}\)

\(m= -6\)

No

(x)

\(\begin{align}\frac{m}{3} = 2\end{align}\)

\(m= 0\)

No

(xi)

\(\begin{align}\frac{m}{3} = 2\end{align}\)

\(m= 6\)

Yes

  
Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school