Question

How do you solve the inequality $2x-7=6+x$ ?

Answer 1

Hint: Now to solve the given equation we will first rearrange the terms of the equation by transposing all the variable terms on LHS and transposing all the constant terms on RHS. Now we will simplify the obtained equation and find the value of x.

Complete step by step solution:
Now we are given with the equation $2x-7=6+x$
We want to find the solution to the equation which means we want to find the value of x for which the given equation is true.
To solve the equation we will first have to arrange the terms.
Now first we will bring all the variable terms on the left hand side.
Hence transposing x from RHS to LHS we get,
$\Rightarrow 2x-7-x=6$
Now we will transpose all the constants from LHS to RHS. Hence we get,
$\Rightarrow 2x-x=6+7$
Now we know that 2x – x = x and 6 + 7 = 13.
Hence on simplifying the above equation we get,
$\Rightarrow x=13$
Hence we get the value of x is 13.
Hence we get x = 13 is the solution of the given equation.

Note: Now note that when we solve a linear equation we can always check the solution by substituting the obtained value of x in the equation and checking of the equation holds. For example on substituting x = 13 in the equation we get LHS = 2x – 7 = 13 × 2 – 7 = 19. And RHS is 6 + x = 13 + 6 = 19. Hence LHS = RHS and the equation holds and the value of x is correct.