Question

How do you solve $2x+8>3x-6$ ?

Answer 1

Hint: To solve the given equation $2x+8>3x-6$ means we need to find the value of $x$ . So, basically we need to place the equal terms one side of equal sign and numbers other side of equal sign. Then, we will solve the equations by doing further processes with use of subtraction and division respectively.

Complete step by step solution:
Since, we have the question as $2x+8>3x-6$ in which we have a variable that is $x$ . So, the question is:
$\Rightarrow 2x+8>3x-6$
Now, we will place equal like terms one side of equal sign and numbers other side of equal sign as:
$\Rightarrow 2x-3x>-6-8$
Now, we will use subtraction for equal like terms and will add the numbers in the above equation so that we can get the value of $x$ as:
$\Rightarrow -x>-14$
Since, the variable is negative in the above equation. So, we will make it positive multiplying by $\left( -1 \right)$ as:
$\Rightarrow -x\times -1>-14\times -1$
As we know that the multiplication of two negative numbers always will be positive and it reverses the symbol of greater than. So, the above equation will be as:
$\Rightarrow x < 14$
Here, we got the value of $x$ . So , according to the above equation we can say that the value of $x$ is less than $14$ that means $-\infty < x < 14$ .
Hence, the solution of the given question is $x < 14$ .

Note: Since, we got the value of variable so we can check if the solution is correct or not in the following way:
Here, we have the question as:
$\Rightarrow 2x+8>3x-6$
L.H.S.:
$\Rightarrow 2x+8$
Now, we will check at $\left( x=13 \right)<14$ as:
$\Rightarrow 2\times 13+8$
Here, we will solve the above equation as:
$\Rightarrow 26+8$
$\Rightarrow 34$
R.H.S.:
$\Rightarrow 3x-6$
Again we will check at $\left( x=13 \right)<14$ as:
$\Rightarrow 3\times 13-6$
Now, we will solve the above equation as:
$\Rightarrow 39-6$
$\Rightarrow 33$
Thus, $L.H.S>R.H.S.$
Hence, $2x+8>3x-6$ . So, the solution is correct.