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.