Question

How do you solve $\dfrac{5w-8}{3}=4w+2$?

Answer 1

Hint: The equation given in the above question is a linear equation in one variable, that is w. The question says that we have to solve the given equation in w. In other words, we have to find the values of w which will satisfy the given equation. Try to find the value of w by performing some mathematical operations.

Complete step-by-step solution:
The given equation says that $\dfrac{5w-8}{3}=4w+2$.
Let us analyse the above equation and try to simplify the equation by performing some mathematical operations on both the sides.
First thing that we can do here is that we can get rid of the fractions and this we can be done by multiplying the LCM of the denominators on both the sides of the equation. In this case, the LCM of the two denominators is 3.
With this the given equation will change to $\dfrac{5w-8}{3}\times 3=(4w+2)\times 3$ …. (i)
If we simplify equation (i), then we get that $5w-8=4w\times 3+2\times 3$.
On simplifying further we get that $5w-8=12w+6$.
Now, we can add 8 on both the sides of the equation and subtract ‘12w’ from both the sides so that the left hand side of the equation gets rid of constant terms and only the terms that are multiple of m are left and on the right hand side only constant terms are left.
On doing this we get that $5w-8+8-12w=12w+6+8-12w$
$\Rightarrow -7w=14$
Now, divide both the sides by (-7).
Therefore,
$\Rightarrow w=\dfrac{14}{-7}=-2$
Hence, the solution of the equation is -2.

Note: Students must note that when we perform mathematical operations on an equation we must keep in mind the equation always holds true. That is why we perform the same operations on both sides. Students must also note that the number of solutions to a given equation in one variable is always less than or equal to the degree of the polynomial in the given equation.