Question

How do you solve -2x+1=-4x+9?

Answer 1

Hint: This type of problem is based on the concept of linear equations with one variable. Here, we first consider the given equation. Add 4x on both the sides of the equation so that we get x terms in the left-hand side of the equation. Then, subtract the whole equation by 1 and make some necessary calculations. And divide both the sides of the equation by 2 to get the value of x which is the required answer.

Complete step by step solution:
According to the question, we are asked to solve -2x+1=-4x+9.
We have been given the equation is -2x+1=-4x+9. -----(1)
Consider the equation (1).
Now, we have to add 4x on both the sides of the equation.
\[\Rightarrow -2x+1+4x=-4x+9+4x\]
We know that terms with the same magnitude and opposite signs cancel out. On cancelling 4x, we get
\[-2x+1+4x=9\]
We have to now group the x terms and add then.
\[\Rightarrow \left( 4-2 \right)x+1=9\]
\[\Rightarrow 2x+1=9\]
Now, we have to subtract 1 from both the sides of the equation.
\[\Rightarrow 2x+1-1=9-1\]
We know that terms with the same magnitude and opposite signs cancel out. On cancelling 1, we get
\[2x=9-1\]
On further simplification, we get
\[2x=8\]
We can express the equation as
\[2x=4\times 2\]
Now, we have to divide the whole equation by 2.
\[\Rightarrow \dfrac{2x}{2}=\dfrac{4\times 2}{2}\]
We find that 2 are common in both the numerator and denominator of both the LHS and RHS.
On cancelling 2, we get
x=4

Therefore, the value of x in the equation -2x+1=-4x+9 is 4.

Note: We can verify whether the answer obtained is correct or not.
Substitute the value of x in the given equation and check whether the LHS is equal to RHS.
Consider equation (2), that is -2x+1=-4x+9.
Here, LHS=-2x+1
But we know that x=4.
Therefore, we get
LHS=-2(4)+1
On further simplifications, we get
LHS=-8+1
Therefore, LHS=-7.
Now consider the RHS.
RHS=-4x+9
On substituting the value of x, we get
RHS=-4(4)+9
On further simplification, we get
RHS=-16+9
Therefore, RHS=-7
Here, LHS=RHS.
Hence the obtained answer is correct.