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Question

Solve.

−2/5x−9<9/10

(2 points)

Answer 1

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.