Question

How do you solve the equation $2x-4+7x < -6x+41$?

Answer 1

Hint: Now to find the solution of the given equation we will first shift all the variable terms from RHS to LHS and all the constant terms from LHS to RHS. Now we will simplify the whole equation and write it in the form of $ax$<$b$. Now we will divide the whole equation by coefficient of x and then hence we will get the solution of the given equation.

Complete step by step solution:
Now we are given with a linear inequality in x.
Now we will solve the equation in the same way we solve linear equalities.
To do so we want to write the inequality in the form $ax$<$b$.
Hence to do so we will rearrange the inequality such that we get all the terms with variable x on LHS and the constant terms on RHS.
Hence we get the equation as,
$\Rightarrow 2x+7x+6x < 41+4$
Now we know that according to distributive property we have 2x + 7x + 6x = (2 + 7 + 6)x = 15x
Hence we get the above equation as,
$\Rightarrow 15x < 45$
Now we have the inequality in the form of $ax=b$ .
Now to solve the inequality we will divide the whole equation by 15. Hence we get the solution as,
$\Rightarrow x < 45$
Hence the solution of the equation is $\left( -\infty ,45 \right)$ .

Note: Now note that for linear equations in one variable we get one particular value for x which satisfies the solution. But when we solve linear inequalities we get a range of solutions or rather a set of infinite solutions. Now here we have the solution set as $\left( -\infty ,45 \right)$ hence all the numbers in the interval are solutions to the given equation.