Question

Solve for x: 3/2+1/2x=2x

Answer 1

Here we will try to solve an equation involving a variable ( x ) given as follows:

`(3)/(2)\text{ + }(1)/(2)\cdot x\text{ = 2x}`

We use the following basic mathematical operations when solving any equation:

`\text{Multiplication, Division, Addition, Subtraction}`

We will first try to isolate our vairable ( x ) on either side of the " = " sign. We will try to isolate ( x ) on the right hand side of " = " sign. To do this we will employ the mathematical operation of " Subtraction ".

We will subtract ( 1 / 2 x ) from both sides of " = " sign:

`\begin{gathered} (3)/(2)\text{ + }(1)/(2)\cdot x\text{ - }(1)/(2)\cdot x\text{ = 2x - }(1)/(2)\cdot x \\ \\ (3)/(2)\text{ = x}\cdot\text{ (}\frac{4\text{ - 1}}{2}) \\ \\ (3)/(2)\text{ = }(3)/(2)\cdot x \end{gathered}`

The next mathematical operation we will apply is " Division ". We will divide the left hand side of the equation with right hand side constant as follows:

`\begin{gathered} x\text{ = }((3)/(2))/((3)/(2)) \\ \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1}} \end{gathered}`

The solution to the given equation is as follows:

`\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1 }}`