I am a a student and I am having difficulty with answering this question. I keep getting the answer wrong. Please may I have a step by step solution to this question so that I won't have difficulties with answering these type of questions in the future.
Solve
$\displaystyle\frac{3x}{4} + \displaystyle\frac{2}{3} = x$
$x$= ____
On
multiplying by $12$ we obtain $$9x+8=12x$$ from here (by sbtracting $9x$) we obtain $$3x=8$$ or $$x=\frac{8}{3}$$
On
One basic concept for you. Hope its help.
Always take variable terms on left side and constant terms on right side. Then solve.
$\frac{3x}{4} - x = \frac{-2}{3}$
$\frac{3x - 4x}{4} = \frac{-2}{3}$
$\frac{-x}{4} = \frac{-2}{3}$
$x = \frac{-2}{3} × - 4$
$x = \frac 83$
On
$$\frac{3x}{4}+\frac{2}{3}=x$$ Notice $\frac{3x}{4}=\frac{3}{4}x$
Now, rewrite the equation as: $$\frac{3}{4}x+\frac{2}{3}=x$$ Now, we need to get our "like terms together. To get our like terms together, we subtract $\frac{3}{4}x$ on both sides. To subtract these, we must find a common denominator. x has a coefficient of 1 in front of it. So, we are subtracting $1x-\frac{3}{4}x$. Or, equivalently (finding a common denominator), we may subtract $$\frac{4}{4}x-\frac{3}{4}x$$. This equals $$\frac{1}{4}x$$ So, now our equation is $$\frac{2}{3}=\frac{1}{4}x$$. We are still trying to isolate x. When x is multiplied by a fraction we may multiply by the reciprocal of the coefficient. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$. Now, we multiply both sides of the equation by $\frac{4}{1}$. This leaves $$\frac{8}{3}=x$$
$$\frac{3x}{4} + \frac23 = x \implies \frac{9x+8}{12} = x \implies 9x+8 = 12 x \implies 8 = 3 x \implies x = \frac83.$$