Question

Determine whether the given value is a solution of the equation

$1-\left[2-\left(3-x\right)\right]=4x-\left(6+x\right)$

(a)$x=2$

(b)$x=4$

Short answer

(a) $x=2$ isa solution

(b)$x=4$ is not a solution

Step-by-step solution

Part a. Step 1. Apply the concept of solutions.

A value is the solution of given equation if upon substituting the value, the equation is satisfied.

Part a. Step 2. Analyze the given expression.

Given

$1-\left[2-\left(3-x\right)\right]=4x-\left(6+x\right)$

To check whether the given value is solution of the equation, we substitute it in place of x.

Part a. Step 3. Solve.

$1-\left[2-\left(3-x\right)\right]=4x-\left(6+x\right)$

Substitute $x=2$

Left Hand Side:

$\begin{array}{l}1-\left[2-\left(3-x\right)\right]\\ =1-\left[2-\left(3-2\right)\right]\\ =1-\left[2-1\right]\\ =1-1\\ =0\end{array}$

Right Hand Side:

$\begin{array}{l}4x-\left(6+x\right)\\ =4\left(2\right)-\left(6+2\right)\\ =8-8\\ =0\end{array}$

Since Left Hand Side is equal to Right Hand Side, $x=2$ is a solution of the equation.

Part b. Step 1. Apply the concept of solutions.

A value is the solution of given equation if upon substituting the value, the equation is satisfied.

Part b. Step 2. Analyze the given expression.

Given

$1-\left[2-\left(3-x\right)\right]=4x-\left(6+x\right)$

To check whether the given value is solution of the equation, we substitute it in place of x.

Part b. Step 3. Solve.

$1-\left[2-\left(3-x\right)\right]=4x-\left(6+x\right)$

Substitute $x=4$

Left Hand Side:

$\begin{array}{l}1-\left[2-\left(3-x\right)\right]\\ =1-\left[2-\left(3-4\right)\right]\\ =1-\left[2+1\right]\\ =1-3\\ =-2\end{array}$

Right Hand Side:

$\begin{array}{l}4x-\left(6+x\right)\\ =4\left(4\right)-\left(6+4\right)\\ =16-10\\ =6\end{array}$

Since Left Hand Side is not equal to Right Hand Side, $x=4$ is not a solution of the equation.