Question

solve by the trial and error method. X+
17=3​

Answer 1

Answer:

Solving an equation means to find the solution of the given equation. A simple equation has an equal (=) sign. This equality shows the balance of both the sides of the equation. The equation remains the same when the expressions are interchanged. There are some methods to solve simple equations.

Trial and Error Method

Substituting different values of the variable and checking the equality of LHS and RHS is the trial and error method. Let us solve the equation 3x + 5 = 17. We start to substitute different values of x. The value for which both the sides are balanced is the required solution.

x LHS = 3x + 5 RHS = 17

1 3x + 5 = 3×1 + 5 = 8 17

2 3x + 5 = 3×2 + 5 =11 17

3 3x + 5 = 3×3 + 5 = 14 17

4 3x + 5 = 3×4 + 5 = 17 17

For x = 4, LHS = RHS. The required solution is x = 4.

Method of Balancing

The equality of both the sides of an equation shows the balance between the two. This balance remains the same even if we add, subtract, multiply or divide both sides of the equation by the same number. Suppose we have to solve, x − 3 = 15. Add 3 to both sides of the equation.

⇒ x − 3 + 3 = 15 + 3 or, x = 18.

Method of Transposing

Transposing means changing the sides of the number in the equation. If a positive number is transposed, it becomes a negative number and vice-versa. The sign of the number gets changed. The basic operators also get changed.

Addition becomes subtraction and vice–versa and the multiplication will become the division and vice–versa. Consider we have an equation, 5x + 14 = 244. We shift the numbers of LHS to RHS.

⇒ 5x = 244 − 14 = 230 or, x = 230 ÷ 5 = 46.

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