Hey! I've been having a lot of trouble with this, please help!
x - 7 > 10
x > __
3x < 20 (underscore under the less / greater than sign)
x < __
5a - 2 < 8
a < __
2t + 8 > 4(t + 1) (underscore under the less/greater than sign)
t > __
I assume you want to solve these inequalities. Just do them the way you would work with equations.
x - 7 > 10
add 7 to both sides:
x > 17
3x <= 20
divide by 3:
x <= 20/3
5a - 2 < 8
add 2, then divide by 5:
5a < 10
a < 2
2t + 8 >= 4(t + 1)
2t + 8 >= 4t + 4
subtract 4 and subtract 2t:
4 >= 2t
2 >= t
or, t <= 2
If you know how to solve equations, you should have no trouble solving inequations.
Just pretend you have an equal sign and use the same steps.
The only exception is: When you multiply or divide both sides by a negative number, you must also reverse the inequality sign
I will do the last one to illustrate
2t + 8 ≥ 4(t + 1)
2t + 8 ≥ 4t + 4 , same as you would for equation
2t -4t ≥ 4 - 8 , same as you would for equation
-2t ≥ -4, still the same steps , BUT NOW:
I have to divide by -2, so do the arithmetic for that
but, I have to reverse the inequality sign
t ≤ 2
check my answer by taking a value of x below 2, then another above 2 in the original inequation.
notice at t = 2, the left side equals the right side
you do the others the same way
Thank you both so much! This helps a lot :)
Sure! I'd be happy to help you with these inequalities.
1. x - 7 > 10:
To solve this inequality for x, we need to isolate the variable x. Let's start by adding 7 to both sides of the equation:
x - 7 + 7 > 10 + 7
This simplifies to:
x > 17
So, the solution to this inequality is x > 17.
2. 3x < 20:
Similarly, to solve this inequality for x, we need to isolate the variable x. In this case, we can do it by dividing both sides of the equation by 3, but we need to be careful when dividing by a negative number because it changes the inequality sign. Since the coefficient of x is positive (3), we don't need to worry about changing the inequality sign. Here's how we solve it:
(1/3)(3x) < (1/3)(20)
x < 20/3
The solution to this inequality is x < 20/3 or x < 6.67 (rounded to two decimal places).
3. 5a - 2 < 8:
To solve this inequality for a, we need to isolate the variable a. Start by adding 2 to both sides of the equation:
5a - 2 + 2 < 8 + 2
Simplifying, we get:
5a < 10
Now, divide both sides of the equation by 5:
(1/5)(5a) < (1/5)(10)
a < 2
So, the solution to this inequality is a < 2.
4. 2t + 8 > 4(t + 1):
To solve this inequality for t, we need to distribute the 4 into the parentheses on the right side of the equation:
2t + 8 > 4t + 4
Now, let's isolate the variable t by subtracting 2t from both sides:
2t - 2t + 8 > 4t - 2t + 4
Simplifying further, we get:
8 > 2t + 4
Next, subtract 4 from both sides of the equation:
8 - 4 > 2t + 4 - 4
This simplifies to:
4 > 2t
Finally, divide both sides of the equation by 2:
(1/2)(4) > (1/2)(2t)
2 > t
So, the solution to this inequality is t < 2.
I hope this explanation helps you understand how to solve these inequalities! Let me know if you have any further questions.