Question

How do you solve $2x+1=10$?

Answer 1

In this question, we are given an equation in terms of x and we need to solve it to find the value of x which satisfies the equation. For this we will try to perform certain arithmetic operations such as addition, subtraction, multiplication, division of numbers on both sides of the equation such that we are left with the variable x on the left side of the equation and a constant on the right side of the equation. The equation will look like x = c where c is the constant. The value of constant will be the required value of x which satisfies the equation.

Complete step by step solution:
Here we are given the equation in terms of x as $2x+1=10$.
We need to solve it to find the value of x which satisfies this equation. For this let us add, subtract, multiply and divide a certain number on both sides of the equation to get an equation of the form x = c. The equation is $2x+1=10$.
As we can see we have a constant 1 on the left side of the equation which we do not want. So let us remove it. For removing the constant 1 let us subtract 1 from both sides of the equation we get $2x+1-1=10-1$.
On the left side of the equation, 1 subtracted from 1 gives 0 and on the right side of the equation 1 subtracted from 10 will give us 9 so our equation reduces to $2x=9$.
The equation is still not in the form of x = c as x has a coefficient 2 so let us remove it.
For removing this constant we need to divide both sides by 2 we get $\dfrac{2x}{2}=\dfrac{9}{2}$.
We know 2 divided by 2 gives 1 so our equation becomes $x=\dfrac{9}{2}$.
As we can see the equation is of the form x = c so the value of x is $\dfrac{9}{2}$ which satisfies the equation.
It can be converted into decimal form or mixed fraction form also. For the decimal form let us multiply numerator and denominator by 5 we get $\dfrac{45}{10}$ which can be written as 4.5. For mixed fraction, we have $2\overset{4}{\overline{\left){\begin{aligned} & 9 \\\ & 8 \\\ & \overline{1} \\\ \end{aligned}}\right.}}$ so mixed fraction becomes $4\dfrac{1}{2}$.

Note: Students can give their answer in any one form- improper fraction, mixed fraction or decimal number. They must take care of signs while adding, subtracting numbers on both sides of the equation. They can also check their answers by following way,
Putting the value of x as $\dfrac{9}{2}$ in the original equation $2x+1=10$ we get $2\left( \dfrac{9}{2} \right)+1=10$.
Cancelling 2 with 2 in first term we get 9+1 = 10.
Simplifying we get 10 = 10.
Left side is equal to the right side therefore $x=\dfrac{9}{2}$ is the correct answer.