Question

How do you solve the equation $2x-3>21$?

Answer 1

Hint: Now we are given with a linear inequality. To solve the inequality we will first separate the variable terms and the constant terms. Now we will divide the whole equation by coefficient of x and then simplify the equation. Hence we get the required condition on x for which the equation holds. Hence we have the solution of the given equation.

Complete step by step solution:
Now we are given with an inequality $2x-3>21$ .
We know that the given inequality is a linear inequality in one variable which is x.
Now we want to find the solution of the given equation.
Hence we will find the values of x for which the equation holds true.
Now we simplify the given inequality the same way we simplify linear equations.
Now first we will separate the variable and constant terms.
Hence we will transpose 3 from LHS to RHS we get $2x>21+3$
Hence on simplifying we get, $2x>24$
Now to find the required condition on x we will divide the whole equation with the coefficient of x which is 2. Hence we get $x>12$
Hence we have the condition on x as $x>12$ hence we can say that the solution of the given equation is $\left( 12,\infty \right)$ .

Note: Now when solving a linear equation remember we just get one solution. But when we have a linear inequality we get a set of solutions for which the inequality if true. We can always check the solution by substituting the values of x and checking if the inequality holds.