Question

Equations The given equation is either linear or equivalent to a linear equation. Solve the equation.

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

Short answer

The solution of the given equation is $x=\frac{1}{17}$.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

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

Step 3. Solve the given equation.

LCM of $2$and$4$ is $4$, so multiply both sides by$4$ to simplify the given equation.

role="math" localid="1643309561504" $$\begin{gathered} 4\left(2x-\frac{x}{2}+\frac{x+1}{4}\right)=4\left(6x\right) \\ 4\left(2x\right)+4\left(-\frac{x}{2}\right)+4\left(\frac{x+1}{4}\right)=24x \\ 8x-2x+x+1=24x \\ 7x+1=24x \end{gathered}$$

Subtract$7x$ from both sides.

$\begin{array}{c}7x+1-7x=24x-7x\\ 1=17x\end{array}$

Divide both sides by $17$.

$$\begin{gathered} \frac{1}{17}=\frac{17x}{17} \\ \frac{1}{17}=x \end{gathered}$$

Thus, the solution of the given equation is $x=\frac{1}{17}$.