How do you solve \frac { 6} { 3} x - 4= 2x + 1?

Jun 5, 2018

no solutions or $\cancel{0}$

Explanation:

$\frac{6}{3} x - 4 = 2 x + 1$

First, add $\textcolor{b l u e}{4}$ to both sides of the equation:
$\frac{6}{3} x - 4 \quad \textcolor{b l u e}{+ \quad 4} = 2 x + 1 \quad \textcolor{b l u e}{+ \quad 4}$

$\frac{6}{3} x = 2 x + 5$

We also know that $\frac{6}{3} = 2$.

$2 x = 2 x + 5$

Subtract $\textcolor{b l u e}{2 x}$ from both sides of the equation:
$2 x \quad \textcolor{b l u e}{- \quad 2 x} = 2 x + 5 \quad \textcolor{b l u e}{- \quad 2 x}$

$0 = 5$

Oh no! Now we don't have any more variables. We have to now see if this equation is true. $0$ does NOT equal to $5$, so the answer is no solutions or $\cancel{0}$.

Hope this helps!