How to solve $\dfrac{7x}{8}+4-\dfrac{2x}{3}=4x-3$?

Question

$$\frac{7x}{8}+4-\frac{2x}{3}=4x-3$$

I do not understand how to simplify this. Could anyone here help me, please? Thanks.

Answer 1

Multiply R.H.S and L.H.S by $24$ to get rid of fractions and calculate $x$

Answer 2

$$\frac{7x}{8}+4-\frac{2x}{3}=4x-3$$

Multiply by the equation by 8 to get rid of the first fraction:

$${7x}+32-\frac{16x}{3}=32x-24$$

Similarly multiply by 3 to get rid of the second fraction:

$${21x}+96-{16x}=96x-72$$

Now you can re-arrange and solve for x.

Collect like terms on both sides:

$$({21x}-{16x}) + 96 =96x-72$$

$$({5x}) + 96 =96x-72$$

Get all terms with x on the left side and all other terms on the right side

$${5x} - 96x = -96-72$$

Simplify:

$$-91x = -168$$

NOTE:

I did the multiplication in 2 steps to show you "baby steps" but you could do it in a single step by finding the Lowest Common Multiple (LCM) of 8 and 3. which gives you 24.