Question

Tell weather -3>-x/5; x =10 is a solution of inequality

Answer 1

Answer:
`\begin{bmatrix}\mathrm{Solution:}\:&\:x>15\:\\ \:\mathrm{Interval\:Notation:}&\:\left(15,\:\infty \:\right)\end{bmatrix}`

Explanation:

`-3>-(x)/(5)`

`-(x)/(5)<-3`

`5\left(-(x)/(5)\right)<5\left(-3\right)`

`-x<-15`

`\left(-x\right)\left(-1\right)>\left(-15\right)\left(-1\right)`

`x>15`

Answer 2

Hey there! :)

To find if the solution is a part of the Inequality, we can do by using two methods.

• Solve The Inequality — ( 1 )
• Substitution and Compare — ( 2 )

Solve The Inequality

We are given the Inequality:

`\displaystyle \large{ - 3 > - (x)/(5) }`

Our goal is to isolate x-term. Since there's 5 as a denominator, what we have to do is to get rid of it by multiplying whole Inequality by 5.

`\displaystyle \large{ - 3 \cdot 5 > - (x)/(5) \cdot 5 } \\ \displaystyle \large{ - 15> - x}`

Since -x is equivalent to -1x.

`\displaystyle \large{ - 15> - 1x}`

Divide both sides by -1. Do not forget to swap the sign from > to < if we are dividing both sides by negative numbers.

`\displaystyle \large{ ( - 15)/( - 1) > ( - 1x)/( - 1) } \\ \displaystyle \large{ 15 < x}`

Switch 15 < x to x > 15.

`\displaystyle \large \boxed{x > 15}`

Since x > 15, that means if we substitute x = 10, we'd get 10 > 15 which is false.

Hence, x = 10 is not a part of the Inequality.

Substitution and Compare

From the Inequality, substitute x = 10 in.

`\displaystyle \large{ - 3 > - (10)/(5) }`

Simplify:

`\displaystyle \large{ - 3 > - 2}`

As we know that -3 is less than -2 and not greater. The Inequality is false.

Therefore, x = 10 is not a part of the solution.

Answer

• x = 10 is not the solution to this Inequaliy.