Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Solve.

−2/5x−9<9/10

(2 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first isolate the variable x.

We can begin by adding 9 to both sides of the inequality:
(-2/5)x - 9 + 9 < 9/10 + 9

Simplifying both sides, we have:
(-2/5)x < 9/10 + 9

Next, we can add the fractions on the right side by finding a common denominator, which is 10:
(-2/5)x < 9/10 + 90/10

Now, we can add the numerators and keep the common denominator:
(-2/5)x < (9 + 90)/10

Simplifying further, we get:
(-2/5)x < 99/10

To get rid of the fraction, we can multiply both sides of the inequality by -10:
-10 * (-2/5)x > -10 * (99/10)

This results in:
(20/5)x > -990/10

Simplifying the right side, we have:
(20/5)x > -99

Further simplification gives:
4x > -99

To finally isolate x, we can divide both sides of the inequality by 4:
(4x)/4 > (-99)/4

This simplifies to:
x > -99/4

Therefore, the solution to the inequality is:
x > -99/4.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the inequality -2/5x - 9 < 9/10, we can follow these steps:

Step 1: Add 9 to both sides of the inequality to eliminate the constant term:
-2/5x - 9 + 9 < 9/10 + 9
-2/5x < 9/10 + 90/10
-2/5x < 99/10

Step 2: Simplify the right side of the inequality:
-2/5x < 99/10

Step 3: Divide both sides of the inequality by -2/5. Since we are dividing by a negative number, the direction of the inequality will reverse:
(-2/5x) / ( -2/5) > (99/10) / ( -2/5)
x > (99/10) / ( -2/5)

Step 4: Simplify the right side of the inequality:
x > (99/10) * ( -5/2)
x > (99 * -5) / (10 * 2)
x > -495/20

Step 5: Simplify the fraction -495/20:
x > -24.75

So the solution to the inequality -2/5x - 9 < 9/10 is x > -24.75.

Answer 3

[AI-generated answer — Explain Bot]

To solve the inequality, −2/5x−9<9/10, we need to isolate the variable x. Here are the steps:

Step 1: Move the constant term to the other side of the inequality.
To do this, we add 9 to both sides of the inequality to cancel out the -9 on the left side:
-2/5x - 9 + 9 < 9/10 + 9/10

Simplifying the right side, we get:
-2/5x < 18/10

Step 2: Simplify the right side.
We can simplify 18/10 by dividing both the numerator and denominator by their greatest common divisor, which is 2:
-2/5x < 9/5

Step 3: Multiply both sides by -5/2.
Multiplying both sides of the inequality by a negative number, -5/2, requires us to reverse the direction of the inequality sign:
(-2/5x)*(-5/2) > (9/5)*(-5/2)

This simplifies to:
x > -9/2

So the solution to the inequality is x > -9/2.

To summarize:
-2/5x - 9 < 9/10
x > -9/2