Question

How do you solve $5x-25>-5$ ?

Answer 1

This question consists of an inequation where we have to find the value of x. Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. The mathematical statement that comprises the inequality sign is known as inequation. Thus, for solving this question, we use the simple inequality method that is we start solving this problem by adding 25 on both sides of the equation. After necessary calculations, we divide both sides by 5 and get the value of x, which is greater than the answer.

Complete step by step answer:
According to the question, we have to find the value of x.
Thus, inequation is $5x-25>-5$ ------- (1)
We solve this question using the simple inequality method.
First, we add 25 on both the sides of the inequation (1), that is
$\Rightarrow 5x-25+25>-5+25$
As we know, the same terms with opposite signs cancel out, thus we get
$\Rightarrow 5x>20$
Now, divide both LHS and RHS by 5 of the above inequation, we get
$\Rightarrow \dfrac{5x}{5}>\dfrac{20}{5}$
Therefore, we get
$\Rightarrow x>4$
Graph for the equation $5x-25>-5$ with the value of $x>4$ is the following.

The above graph shows that the value of x will take all values, which lie in the shaded region. Since $x>4$ implies x is not equal to 4 that is why in the graph, we have shown the value 4 as a big empty circle and not a shaded circle.
It implies that x will take values greater than 4. Thus, for the equation $5x-25>-5$ , the value of x is $5,6,...7.4,10.1,....11.9...$ and so on.

Note: Always remember the difference between greater than sign and greater than equal to sign in inequality questions. One of the alternative methods is you can start this question by removing the negative sign, then apply distributive property $-a(b-c)=-ab+ac$ on the LHS of the inequation and subtract 25 on both sides. After necessary calculations, again multiply both sides by (-1) and in the last divide both the sides by 5 to get the required answer, which is the value of x.
An Alternative method:
Inequation is $5x-25>-5$ ----- (2)
Now multiply both the sides by (-1) in inequation (2), we get
$\Rightarrow (-1).(5x-25)>-5.(-1)$
Let us apply distributive property $-a(b-c)=-ab+ac$ on the left side of the above inequation, we get
$\begin{aligned} & \Rightarrow (-1)(5x)+(1).(25)>5 \\\ & \Rightarrow -5x+25>5 \\\ \end{aligned}$
Now, subtract 25 on both sides of the above inequation, to get
$\Rightarrow -5x+25-25>5-25$
As we know, the opposite sign of the same terms cancels out, thus we get
$\Rightarrow -5x>-20$
Now, again multiply both sides by (-1), we get
$\begin{aligned} & \Rightarrow -5x.(-1)>-20.(-1) \\\ & \Rightarrow 5x>20 \\\ \end{aligned}$
Divide both sides by 5, we get
$\Rightarrow \dfrac{5x}{5}>\dfrac{25}{5}$
Therefore, we get
$\Rightarrow x>4$
Thus, x will take values $5,6,....10,...11.5...$ , which is our required answer.