# PracticeExponential Inequality 3

#### MarkFL

##### La Villa Strangiato
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Math Helper
Write the RHS as a power of 5...

Staff member
Moderator
Math Helper
Yes.

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
You can't just replace 125 with 5...what you must do is as follows:

$$\displaystyle 5^{2x}<125^{x-5}$$

$$\displaystyle 5^{2x}<(5^3)^{x-5}$$

$$\displaystyle 5^{2x}<5^{3(x-5)}$$

$$\displaystyle 5^{2x}<5^{3x-15}$$

#### pre-trip_rapture

##### Member
You can't just replace 125 with 5...what you must do is as follows:

$$\displaystyle 5^{2x}<125^{x-5}$$

$$\displaystyle 5^{2x}<(5^3)^{x-5}$$

$$\displaystyle 5^{2x}<5^{3(x-5)}$$

$$\displaystyle 5^{2x}<5^{3x-15}$$
I made a typo. I know that 125 = 5^3.

#### pre-trip_rapture

##### Member
You can't just replace 125 with 5...what you must do is as follows:

$$\displaystyle 5^{2x}<125^{x-5}$$

$$\displaystyle 5^{2x}<(5^3)^{x-5}$$

$$\displaystyle 5^{2x}<5^{3(x-5)}$$

$$\displaystyle 5^{2x}<5^{3x-15}$$
2x < 3x - 15

2x - 3x < - 15

-x < - 15

x < - 15/-1

x < 15

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
When you multiply/divide both sides of an inequality by a negative number, the direction of the inequality must change.

pre-trip_rapture

#### pre-trip_rapture

##### Member
When you multiply/divide both sides of an inequality by a negative number, the direction of the inequality must change.
Yes. I forgot this rule.

2x < 3x - 15

2x - 3x < - 15

-x < - 15

x > - 15/-1

x > 15

MarkFL

Staff member