Solveeit Logo
Login

Question

Question: How do you solve \(2x-4=5x+17\) ?...

How do you solve 2x−4=5x+172x-4=5x+17 ?

Explanation

Solution

In this question, we have to find the value of x. Since, the given equation is linear, because it consists of only one variable and many constants. Thus, to solve this problem, we first add 4 on both sides of the equation and then make the necessary calculations. Then, we will subtract 5x on both sides of the equation and combine the like terms. After that, we will divide 3 on both sides of the equation and make the necessary calculations. In the last, we multiply both sides by (-1), to get the value of x, which is our required answer.

Complete answer:
According to the problem, we have to find the value of x.
So, we simply follow a few steps to get our answer.
The equation given to us is 2x−4=5x+172x-4=5x+17 ------------- (1)
Firstly, we will add 4 on both sides in the equation (1), we get
⇒2x−4+4=5x+17+4\Rightarrow 2x-4+4=5x+17+4
Now, the same terms with opposite signs cancel out each other on the left-hand of the above equation, therefore we get
⇒2x=5x+17+4\Rightarrow 2x=5x+17+4
On further simplification, we get
⇒2x=5x+21\Rightarrow 2x=5x+21
Now, we will subtract 5x5x on both sides in the above equation, we get
⇒2x−5x=5x+21−5x\Rightarrow 2x-5x=5x+21-5x
As we know, the same terms with opposite signs cancel out each other on the right-hand of the above equation, thus we get
⇒2x−5x=21\Rightarrow 2x-5x=21
Now, we will combine like terms on the LHS in the above equation, we get
⇒−3x=21\Rightarrow -3x=21
Now, we will divide 3 on both sides of the equation, we get
⇒−33x=213\Rightarrow \dfrac{-3}{3}x=\dfrac{21}{3}
On further solving, we know that in the division if the numerator and the denominator are the same, then they will cancel out to 1, therefore we get
⇒−1.x=213\Rightarrow -1.x=\dfrac{21}{3}
In the RHS of the above equation, both the numerator and denominator are the factors of 3, we get
⇒−x=7\Rightarrow -x=7
So, we will multiply (-1) on both sides of the above equation, we get
⇒−x.(−1)=7.(−1)\Rightarrow -x.(-1)=7.(-1)
Therefore, on further simplification we get
⇒x=−7\Rightarrow x=-7
Therefore, for the equation 2x−4=5x+172x-4=5x+17 , the value of x is equal to -7, which is our required answer.

Note: Make all the necessary calculations properly to avoid mistakes. One of the alternative methods is after the 2x=5x+212x=5x+21 step, subtract both sides of the equation by 2x, then cancel out the same terms with opposite signs. After that, again subtract 21 on both sides of the equation and then divide 3 on both sides to get the value of x, which is our required answer.