Question

How do you solve $3x-4=2x+8-5x$?

Answer 1

Hint: In this question, we are given an equation in terms of x and we need to find the value of x which satisfies the equation. For this we will apply operation (addition, subtraction, multiplication, division) step by step to get an equation such that variable x is left on the left side of the equation and a constant term on the right side of the equation. The value of the constant will be the required value of x.

Complete step by step answer:
Here we are given the equation as $3x-4=2x+8-5x$.
We need to solve it to find the value of x which satisfies the given equation.
Let us first simplify the equation by solving for like terms. We can see the right side of the equation has like terms 2x and -5x which can be solved to reduce a term. We need to solve 2x-5x. We know that 5-2 is equal to 3 but negative sign is with 5 which is greater so we have 2-5 = -3 and 2x-5x = -3x. The equation thus reduces as $3x-4=-3x+8$.
Now let us reduce the equation in the form as x = c where c is constant.
As we do not want any constant on the left side of the equation. So, let us remove it. For removing 4 let us add 4 on both sides of the equation we get $3x-4+4=-3x+8+4$.
Simplifying the constant terms on both sides, we get the equation as $3x=-3x+12$.
As there is a variable term on the right side of the equation, so let us remove it. For this let us add 3x on both sides of the equation we get $3x+3x=-3x+12+3x$.
On the right side 3x cancels out with -3x we get $3x+3x=12$.
On the left side we see that we have like terms which can be added. So adding 3x with 3x we get $3x+3x=\left( 3+3 \right)x=6x$.
The equation becomes 6x = 12.
The equation is not of the form x = c as we have a coefficient of x as 6. So let us remove it. For removing the coefficient let us divide both sides of the equation by 6 we get $\dfrac{6x}{6}=\dfrac{12}{6}$.
We know that 6 divided by 6 gives 1 and 12 divided by 6 gives 2 so we get x = 2.
Which is of the form x = c.

Hence the required value of x is equal to 2.

Note: Students should take care of the signs while solving the equation. Take care while applying operation on both sides of the equation. Students can also check their answer by putting the value of x as 2 in the original equation i.e. $3\left( 2 \right)-4=2\left( 2 \right)+8-5\left( 2 \right)$.
Solving we get $6-4=4+8-10\Rightarrow 2=12-10\Rightarrow 2=2$.
Left side is equal to the right side so x = 2 is the correct answer.