Which of the following are simple equations? (i) 3x + 5 = 14 (ii) 3x - 6 = x + 2 (iii) 3 = 2x + y (iv) (x/3) + 5 = 0 (v) x² + 5x + 3 = 0 (vi) 5m - 6n = 0 (vii) 7p + 6q + 13s = 11 (viii) 13t - 26 = 39
Answer (1)
To determine which of the given options are simple equations, let's first define what a simple equation is. In mathematics, a simple equation typically involves only one variable and contains algebraic expressions that are set equal to each other. They may have operations such as addition, subtraction, multiplication, and division, but do not include exponents greater than 1 or multiple variables combined.
Let's evaluate each given statement:
(i) 3 x + 5 = 14 This is a simple equation as it contains one variable x and linear operations.
(ii) 3 x − 6 = x + 2 This is also a simple equation. It has one variable, x , and involves linear operations. The equation can be simplified to solve for the variable.
(iii) 3 = 2 x + y This is not considered a simple equation for one variable because it involves two different variables, x and y .
(iv) 3 x + 5 = 0 This is a simple equation. It has one variable, x , and involves basic arithmetic operations.
(v) x 2 + 5 x + 3 = 0 This is not a simple equation because it is a quadratic equation due to the presence of x 2 .
(vi) 5 m − 6 n = 0 This is not considered a simple equation because it contains two variables, m and n .
(vii) 7 p + 6 q + 13 s = 11 This is not a simple equation, as there are three variables involved, p , q , and s .
(viii) 13 t − 26 = 39 This is a simple equation as it involves one variable, t , and basic arithmetic operations.
In conclusion, the simple equations among the given options are: (i) 3 x + 5 = 14 (ii) 3 x − 6 = x + 2 (iv) 3 x + 5 = 0 (viii) 13 t − 26 = 39
