Question

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

Answer 1

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

Step-by-step explanation:

$-3>-\frac{x}{5}$

$-\frac{x}{5}$

$5\left(-\frac{x}{5}\right)$

$-x$

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

$x>15$

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:

$\displaystyle \large{ - 3 > - \frac{x}{5} }$

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.

$\displaystyle \large{ - 3 \cdot 5 > - \frac{x}{5} \cdot 5 } \\ \displaystyle \large{ - 15> - x}$

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.

$\displaystyle \large{ \frac{ - 15}{ - 1} > \frac{ - 1x}{ - 1} } \\ \displaystyle \large{ 15 < x}$

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.

$\displaystyle \large{ - 3 > - \frac{10}{5} }$

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.