1. x - 7 > 10
x > 17
2. 3x <= 21
x <= 7
3. 5a - 2 < 18
a < 4
4. 2t + 8 >= -4(t + 1)
t >= -2
correct
Corrected it so fast? :)
Just happened to be up, and saw it come in. Good work.
To solve each of these inequalities, we need to isolate the variable on one side of the inequality sign. Here's how to solve each of the given inequalities:
1. x - 7 > 10
Start by adding 7 to both sides of the inequality:
x - 7 + 7 > 10 + 7
Simplify:
x > 17
2. 3x <= 21
Divide both sides of the inequality by 3 (since the coefficient of x is positive):
(3x)/3 <= 21/3
Simplify:
x <= 7
3. 5a - 2 < 18
Start by adding 2 to both sides of the inequality:
5a - 2 + 2 < 18 + 2
Simplify:
5a < 20
Then, divide both sides of the inequality by 5 (since the coefficient of a is positive):
(5a)/5 < 20/5
Simplify:
a < 4
4. 2t + 8 >= -4(t + 1)
Start by simplifying the right side of the inequality using the distributive property:
2t + 8 >= -4t - 4
Next, combine like terms by adding 4t to both sides of the inequality:
2t + 4t + 8 >= -4t + 4t - 4
Simplify:
6t + 8 >= 0
Now, subtract 8 from both sides of the inequality:
6t + 8 - 8 >= 0 - 8
Simplify:
6t >= -8
Finally, divide both sides of the inequality by 6 (since the coefficient of t is positive):
(6t)/6 >= (-8)/6
Simplify:
t >= -2
These are the solutions to the given inequalities. If you follow these steps, you'll be able to solve similar inequalities in the future.