Solve.and show your work

−2/5x−9<9/10

Solve.

4x+6<−6

Solve.

q+12−2(q−22)>0

I will do the more complicated looking one, you try the others

(−2/5)x−9<9/10
The LCD is 10, so let's multiply each term by +10, no need to reverse the inequality sign
-4x - 90 < 9
add 90 to both sides
-4x < 99
divide both sides by -4, note the reversal of the inequality sign since we divided by a negative
x > -99/4 or x > -24.75 if you prefer decimals

Alright, let's solve these equations and have some fun while doing it!

For the first equation, we have:

-2/5x - 9 < 9/10

To isolate x, we can start by adding 9 to both sides:

-2/5x < 9/10 + 9

Now let's find a common denominator for the right side:

-2/5x < 9/10 + 90/10

Combining the fractions:

-2/5x < 99/10

To get rid of the fractional coefficient (-2/5), we can multiply both sides by its reciprocal (5/2):

(-2/5x) * (5/2) > (99/10) * (5/2)

Simplifying:

x > 495/20

Reducing the fraction:

x > 99/4

So, the solution is x > 99/4. Keep in mind that you can also express it as a decimal (24.75).

Now, let's move on to the second equation:

4x + 6 < -6

To isolate x, let's subtract 6 from both sides:

4x < -6 - 6

Simplifying:

4x < -12

Dividing both sides by 4:

x < -12/4

Reducing the fraction:

x < -3

So, the solution for the second equation is x < -3. Easy-peasy-lemon-squeezy!

Finally, let's tackle the third equation:

q + 12 - 2(q - 22) > 0

We can start by simplifying the equation inside the parentheses:

q + 12 - 2q + 44 > 0

Now, let's combine like terms:

-q + 56 > 0

To isolate q, we need to get rid of that pesky positive 56. Let's subtract 56 from each side:

-q > -56

But wait, multiplying both sides by -1 will give us a positive q:

q < 56

So, the solution for the third equation is q < 56. You got this!

I hope that brought a smile to your face while solving these equations. Remember, math doesn't have to be boring!

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

Step 1: Move the constant term to the right side of the inequality:
−(2/5)x < 9/10 + 9

Step 2: Simplify the right side of the inequality:
−(2/5)x < 9/10 + 90/10
−(2/5)x < 99/10

Step 3: Multiply both sides of the inequality by the reciprocal of the coefficient of x, which is −5/2 (to keep the inequality sign the same):
−5/2 * −(2/5)x > −5/2 * (99/10)
x > -495/20

Step 4: Simplify the right side of the inequality:
x > -24.75

Therefore, the solution to the inequality is x > -24.75.

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To solve the inequality 4x + 6 < −6, we will follow the steps below:

Step 1: Move the constant term to the right side of the inequality:
4x < −6 - 6

Step 2: Simplify the right side of the inequality:
4x < −12

Step 3: Divide both sides of the inequality by the coefficient of x, which is 4 (remember that dividing by a negative number reverses the inequality sign):
(4x) / 4 > (-12) / 4
x > -3

Therefore, the solution to the inequality is x > -3.

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To solve the inequality q + 12 - 2(q - 22) > 0, we will follow these steps:

Step 1: Distribute the -2 to the terms inside the parentheses:
q + 12 - 2q + 44 > 0

Step 2: Combine like terms:
-q + 56 > 0

Step 3: Move the constant term to the right side of the inequality:
-q > -56

Step 4: Divide both sides of the inequality by -1 (remember that dividing by a negative number reverses the inequality sign):
q < -56 / -1
q < 56

Therefore, the solution to the inequality is q < 56.

Sure! Let's solve these equations step by step.

Question 1: Solve the inequality -2/5x - 9 < 9/10

Step 1: To solve this inequality, we'll start by isolating the variable x. Let's begin:

-2/5x - 9 < 9/10

Step 2: To eliminate the fraction, we'll multiply both sides of the inequality by the common denominator of 10:

10 * (-2/5x - 9) < 10 * (9/10)

-4x - 90 < 9

Step 3: Now, let's isolate x by moving the constant term (-90) to the other side of the inequality:

-4x < 9 + 90

-4x < 99

Step 4: To solve for x, divide both sides of the inequality by -4. However, keep in mind that when we divide both sides of an inequality by a negative number, the direction of the inequality sign flips.

x > 99 / -4 (Remember to change the direction of the inequality)

x > -24.75

So, the solution to the inequality is x > -24.75.

Question 2: Solve the inequality 4x + 6 < -6

Step 1: To solve this inequality, we'll start by isolating the variable x. Let's begin:

4x + 6 < -6

Step 2: Now, let's isolate x by moving the constant term (6) to the other side of the inequality:

4x < -6 - 6

4x < -12

Step 3: To solve for x, divide both sides of the inequality by 4:

x < -12 / 4

x < -3

So, the solution to the inequality is x < -3.

Question 3: Solve the inequality q + 12 - 2(q - 22) > 0

Step 1: Let's start by simplifying the expression inside the brackets first:

q + 12 - 2q + 44 > 0

Step 2: Combine like terms:

-q + 56 > 0

Step 3: Now, let's isolate q by moving the constant term (56) to the other side of the inequality:

-q > -56

Step 4: To solve for q, divide both sides of the inequality by -1. Remember, when you divide both sides by a negative number, the direction of the inequality sign flips:

q < -56

So, the solution to the inequality is q < -56.

I hope this helps! Let me know if you have any other questions.