Question

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

Solve.
2
9
5
X — 9 < -
10

Answer 1

To solve the inequality
`\(-(2)/(5)x - 9 < (9)/(10)\)`, add 9 to both sides, combine fractions, multiply by
`\(-(5)/(2)\)` and flip the inequality sign, simplify, and reduce the fraction to find that the solution is
`\(x > -24.75\)`.

Step-by-step explanation:

To solve the inequality
`-\((2)/(5)x - 9 < (9)/(10)\)`, we will follow these steps:

Add 9 to both sides of the inequality to get
`\(-(2)/(5)x < (9)/(10) + 9\)`.

Convert 9 to a fraction with a denominator of 10 to combine it with
`\((9)/(10)\)`, which gives us
`\(-(2)/(5)x < (9)/(10) + (90)/(10)\)`.

Combine the fractions on the right side to get
`\(-(2)/(5)x < (99)/(10)\)`.

Multiply both sides by
`\(-(5)/(2)\)` to isolate x, remembering to reverse the inequality because we are multiplying by a negative number, giving us
`\(x > (99)/(10) * (-(5)/(2))\)`.

Simplify the right side to find the solution for x, which is
`\(x > -(495)/(20)\)`.

Reduce the fraction to its simplest form to get the final answer,
`\(x > -24.75\)`.

The solution to the inequality is all real numbers greater than -24.75.

Answer 2

To solve the inequality
`-(2)/(5)x - 9 < (9)/(10)`, isolate the variable x by sequentially adding 9, finding a common denominator, summing fractions, multiplying by the inverse, and simplifying the resulting fraction, leading to the the fraction to get the final answer:
`x \geq (495)/(20)` which simplifies to
`x \geq 24.75`..

Step-by-step explanation:

To solve the inequality
`-(2)/(5)x - 9 \leq (9)/(10)`, we first aim to isolate the variable x on one side. Here are the steps you would follow to do this:

Add 9 to both sides of the inequality to get: -
`(2)/(5)x \leq (9)/(10) + 9`.

Convert 9 to a fraction with a common denominator of 10 to obtain: -
`(2)/(5)x \leq (9)/(10) + (90)/(10)`.

Sum the fractions on the right side to get: -
`(2)/(5)x \leq (99)/(10)`.

Multiply both sides of the inequality by -
`(5)/(2)` and reverse the inequality sign (since we multiply by a negative number), resulting in:
`x \geq -(99)/(10) * -(5)/(2)`.

Simplify the right side by multiplying the numerators and denominators separately to find the value of x:

`x \geq (99 * 5)/(10 * 2)`.

Simplify the fraction to get the final answer:
`x \geq (495)/(20)` which simplifies to
`x \geq 24.75`.