Question

Determine whether the values are solutions to the equation: $4x-2=2x+1$.

(a)$x=\frac{3}{2}$(b)$x=-\frac{1}{2}$

Short answer

Part (a) $x=\frac{3}{2}$is a solution to the equation.

Part (b) $x=-\frac{1}{2}$is not a solution to the equation.

Step-by-step solution

Part (a) Step 1. Given information.

Determine whether the values are solutions to the equation: $4x-2=2x+1$.

(a) $x=\frac{3}{2}$(b)$x=-\frac{1}{2}$

Part (a) Step 2. Substitute the value x=32 in the equation.

$$\begin{gathered} 4x-2=2x+1 \\ 4\left(\frac{3}{2}\right)-2=2\left(\frac{3}{2}\right)+1 \\ 2·3-2=1·3+1 \\ 6-2=3+1 \\ 4=4 \end{gathered}$$

Thus $x=\frac{3}{2}$result in a true equation.

Hence, $x=\frac{3}{2}$is a solution of the equation.

Part (b) Step 3. Substitute the value x=-12 in the equation.

$$\begin{gathered} 4x-2=2x+1 \\ 4\left(-\frac{1}{2}\right)-2=2\left(-\frac{1}{2}\right)+1 \\ 2·(-1)-2=1·(-1)+1 \\ -2-2=-1+1 \\ -4\ne 0 \end{gathered}$$

Thus $x=-\frac{1}{2}$does not result in a true equation.

Hence, $x=-\frac{1}{2}$is not a solution of the equation.