Question

How do you solve – 39 $\le $ 5x – 9 ?

Answer 1

Hint: From the given equation we know that 5x – 9 is greater than – 39 , now we can add 9 to both LHS and RHS and to evaluate the range of 5x. From the range of 5x we can find out the range of x which will satisfy the given inequality.

Complete step by step answer:
The given inequality is – 39 $\le $ 5x – 9 , we know that we can add any constant to both LHS and RHS. The equation will not change. We can add 9 both sides so that we can evaluate the range of 5x.
So by adding 9 both sides we get -30 $\le $ 5x , Now dividing LHS and RHS by 5 we can write – 6 $\le $ x.
So the range of x is $\left[ -6,\infty \right)$ , $x\in \left[ -6,\infty \right)$ is the solution of – 39 $\le $ 5x – 9 .

Note:
When we solve - 30 $\le $ 5x and find the range of x, we simply divide both sides by 5. But instead of 5 if we have some negative number then we should change the inequality sign. For example, if -3x > 6 then x is less than -2 that means x < -2. So, if we divide or multiply any negative number to an inequality, then we should change the inequality sign and keep in mind that we can not multiply or divide 0 on both sides.