Solved on Jan 18, 2024

Solve the inequality $4x-5<0$ for real values of $x$ .

STEP 1

Assumptions
1. We are given an inequality $4x - 5 < 0$ .
2. We need to solve for the variable $x$ .

STEP 2

To solve for $x$ , we want to isolate $x$ on one side of the inequality. We can start by adding $5$ to both sides of the inequality to move the constant term to the right side.
$4x - 5 + 5 < 0 + 5$

STEP 3

Simplify both sides of the inequality.
$4x < 5$

STEP 4

Now, we need to divide both sides of the inequality by $4$ to solve for $x$ .
$\frac{4x}{4} < \frac{5}{4}$

STEP 5

Simplify both sides of the inequality.
$x < \frac{5}{4}$

STEP 6

We have isolated $x$ and found the solution to the inequality.
The solution is $x < \frac{5}{4}$ or $x < 1.25$ .

Was this helpful?

Solve the inequality $4x-5<0$ for real values of $x$ .

STEP 1

Assumptions
1. We are given an inequality $4x - 5 < 0$ .
2. We need to solve for the variable $x$ .

STEP 2

To solve for $x$ , we want to isolate $x$ on one side of the inequality. We can start by adding $5$ to both sides of the inequality to move the constant term to the right side.
$4x - 5 + 5 < 0 + 5$

STEP 3

Simplify both sides of the inequality.
$4x < 5$

STEP 4

Now, we need to divide both sides of the inequality by $4$ to solve for $x$ .
$\frac{4x}{4} < \frac{5}{4}$

STEP 5

Simplify both sides of the inequality.
$x < \frac{5}{4}$

STEP 6

We have isolated $x$ and found the solution to the inequality.
The solution is $x < \frac{5}{4}$ or $x < 1.25$ .

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the inequality 4x−5<04x-5<04x−5<0 for real values of xxx.

STEP 1

Assumptions1. We are given an inequality 4x−5<04x - 5 < 04x−5<0.2. We need to solve for the variable xxx.

STEP 2

To solve for xxx, we want to isolate xxx on one side of the inequality. We can start by adding 555 to both sides of the inequality to move the constant term to the right side.4x−5+5<0+54x - 5 + 5 < 0 + 54x−5+5<0+5

STEP 3

Simplify both sides of the inequality.4x<54x < 54x<5

STEP 4

Now, we need to divide both sides of the inequality by 444 to solve for xxx.4x4<54\frac{4x}{4} < \frac{5}{4}44x​<45​

STEP 5

Simplify both sides of the inequality.x<54x < \frac{5}{4}x<45​

STEP 6

We have isolated xxx and found the solution to the inequality.The solution is x<54x < \frac{5}{4}x<45​ or x<1.25x < 1.25x<1.25.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the inequality $4x-5<0$ for real values of $x$ .

Assumptions
1. We are given an inequality $4x - 5 < 0$ .
2. We need to solve for the variable $x$ .

To solve for $x$ , we want to isolate $x$ on one side of the inequality. We can start by adding $5$ to both sides of the inequality to move the constant term to the right side.
$4x - 5 + 5 < 0 + 5$

Simplify both sides of the inequality.
$4x < 5$

Now, we need to divide both sides of the inequality by $4$ to solve for $x$ .
$\frac{4x}{4} < \frac{5}{4}$

Simplify both sides of the inequality.
$x < \frac{5}{4}$

We have isolated $x$ and found the solution to the inequality.
The solution is $x < \frac{5}{4}$ or $x < 1.25$ .