Linear Equations Test - 1

7x + 10 = 0, is a linear equation. Because it does not contain any produced term, and the degree is 1.

None of the given equations are linear equations, because in each equation, there is a product term, and hence the degree is not 1.

Let the number be x
3x = 72
x = 24
5 times the number = 5 × 24 = 120.

Let Sid's age = x years
2x = 32
x = 16 years
Five times Sid's age = 16 × 5 = 80 years

Let the weight of child = x kg
3x = 36
x = 12 kg

Let width = x cm
Length = 4x cm
Area = x × 4x = 4x² cm²
4x² = 64
x² = 16 ⇒ x = 4 cm

Let Leah's sister's age = x years
Leah's age = 2x – 4
According to question,
x + 2x – 4 = 20
3x = 24
x = 8 years
Leah's age = 8 × 2 – 4
= 12 years

Let Jack's present age = x years
Jack's age after 2 years = (x + 2) years
According to question,
5 (x + 2) = 100
x + 2 = 20
x = 18

Let Charlie's present age = x years
Millie's present age = (40 – x) years
Fourteen years ago,
Charlie's age = (x – 14) years
Millie's age = (40 – x – 14)
= (26 – x) years
According to question,
(26 – x) = 2(x – 14)
26 – x = 2x – 28
3x = 54
x = 18
x = 18 years
Therefore, Charlie's present age = 18 years and
Mille's present age = 40 – 18 = 22 years

Let Richa's present age = x years
Dorothy's present age = (x + 6) years
Product of their ages = x(x + 6) years
6 years ago,
Richa's age = (x – 6) years
Dorothy's age = x + 6 – 6 = x years
Product of their ages = (x) (x – 6) years
According to question,
(x) (x + 6) = 2 (x) (x – 6)
x + 6 = 2x – 12
x = 18 years
Therefore, Dorothy's present age = 18 + 6 = 24 years

x + 3y = 5 is not a linear equation in one variable.

7 - 2x + 3y = 0
Standard form
⇒- 2x + 3y + 7 = 0

x = 4 is a linear equation because the degree of x is 1 and it does not include any product term.