Question

How do you solve 15x + 5 > 10x – 25.

Answer 1

Hint: To solve the given inequality we will first bring 10x to LHS and 5 to RHS. Now we will subtract the terms and divide the whole equation with coefficient of x in the obtained equation. Hence we will get the value of x and hence the solution of the given inequality.

Complete step-by-step solution:
Now to solve the inequality we will first bring all the variable terms on LHS and the constants on RHS.
Now consider the given expression 15x + 5 > 10x – 25.
Let us transpose 10x from RHS to LHS. Since we are shifting the term on opposite side its sign will change
Hence we get the equation as 15x – 10x + 5 > – 25.
Now let us transpose 5 from LHS to RHS. Again its sign will change accordingly.
Hence we get the equation as 15x – 10x > –25 – 5
Now we have all the variable terms on one side and all the constants on the other side hence we can solve the equation.
Now subtracting the terms we get 5x > - 30.
Now let us divide the whole equation by 5. Since 5 > 0 the sign will not change.
Hence after division we get x > - 6.
Hence the equation is true for all x > - 6
Hence the solution set of the equation is $\left( -6,\infty \right)$.

Note: Note that while solving inequality most of the rules are the same as solving equalities but not for multiplication or division. If we multiply or divide the whole equation by a positive number then the sign of inequalities does not change. If we multiply or divide the whole equation by a negative number then the sign of inequality changes.