Mathematics
Grade-8
Easy

Question

The teacher asked the student to give a statement for the linear equation, the response she got is “ twice of five times a number is added with 3 is same as ten times a number being added to 6.” The number for the above statement is

  1. for any number the equation satisfies
  2. for any number the equation dissatisfies
  3. the number is 4
  4. the number is 6

hintHint:

An equation has a constant, variable and an equal to sign. It has two sides LHS and RHS. A linear equation in one variable is equation with only one variable and in which the highest degree is 1. Here, we have to find the value of unknown value, by operating both sides with the same number so that the equation will be balanced.

The correct answer is: for any number the equation satisfies


In the question it is given that twice of five times a number is added with 3 is same as ten times a number being added to 6.
We have to find the number.
Step 1: Convert the given word problem into numerical equation.
Let the unknown number be x.
So, the equation will be
2(5x+3)= 10x+6
Step 2: Solve the bracket on LHS side.
10x+6= 10x+6
Here, the variable and constant terms are same on both sides, which on solving will give 0=0. So, this equation has infinitely many solutions.
Therefore, the correct option is a, i.e., for any number the equation satisfies.

The linear equations with one variable are an equation which has only one variable and the highest power of the variable should be one. The linear equations in one variable having infinitely many solutions if it has same variable and constant terms on both the sides of the equation. On solving the equation, they will get cancelled and will give 0=0 as result.

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