Q. 3x − 5 = 7. Check if x = 4 is a root or zero or solution of this linear equation in 1 variable.

3(4) = 7

12 − 5 = 7

7 = 7

LHS = RHS

A value is a solution of an equation in 1 variable if, after substitution

LHS = RHS i.e. it forms a true equality.

∴ Yes, x = 4 is a solution of the equation

3x − 5 = 7.

Q. x = 3, 5 + 3x = 14. Check if the first equation intersects with the second equation.

Q.

∴ Substituting the value of 1 variable in the other equation, and checking if it forms a true equality.

⇒ 5 + 3(3) = 14

⇒ 5 + 9 = 14

⇒ 14 = 14

LHS = RHS

∴ x = 3 is a solution of the equation

5 + 3x = 14.

Q. Check if x = 2 is a zero of 3x − 2 = 8x + 12

Q. 

If value of x as 2 is a solution of the given equation, then left hand side must equal right hand side value, after substitution.

⇒ 3(2) − 2 = 8(2) + 12

⇒ 6 − 2 = 16 + 12

⇒ 4 = 28

LHS ≠ RHS

∴ x = 2 is not a root of the equation

3x − 2 = 8x + 12.

Q. Check if x = 2 is a zero of 3x − 2 = 8x − 12

∴ After substituting the value, it must form a true equality.

⇒ 3(2) − 2 = 8(2) − 12

⇒ 6 − 2 = 16 − 12

⇒ 4 = 4

LHS = RHS

⇒ x = 2 is a solution/zero/root of the equation

3x − 2 = 8x − 12.

Q. Check if x = 4 is a solution of 3x/2 = 6.

Q.

∴ If we substitute the value of x as 4 in the given equation, it must form a true equality.

⇒ 3(4)/2 = 6

⇒ 12/2 = 6

⇒ 6 = 6

LHS = RHS

∴ Yes, x = 4 is a root of the given equation.

Q.  Check if x = 2 satisfies x − 3 = 2x − 5.

Q.

If x = 2 is true for the given equation, then if we substitute the value of variable, the final equality must also be true.

⇒ (2) − 3 = 2(2) − 5

⇒ −1 = 4 − 5

⇒ −1 = −1

LHS = RHS

∴ Yes x = 2 is a solution/root/zero of the given equation

x − 3 = 2x − 5.

Q. Check if x = 8 is a root/zero of x/2 + 7 = 11.

Q.

Truth of the final equality determined by substituting the value of variable x as 8, means x = 8 is a solution/root/zero of that equation.

⇒ (8/2) + 7 = 11

⇒ 4 + 7 = 11

⇒ 11 = 11

LHS = RHS (True equality)

∴ x = 8 is a solution of x/2 + 7 = 11.