Write two different inequalities that you can solve by adding 5 and multiplying by -3.
-x/3 - 5 < 12
To solve an inequality by adding 5 and multiplying by -3, you need to isolate the variable on one side of the inequality sign. Here are two different examples:
1. Inequality 1:
Start with any inequality, for example, x + 3 < 7.
First, subtract 3 from both sides of the inequality:
x + 3 - 3 < 7 - 3
x < 4
Then, add 5 to both sides:
x + 5 < 4 + 5
x + 5 < 9
Finally, multiply both sides by -3:
-3(x + 5) > -3(9)
-3x - 15 > -27
This results in the inequality: -3x > -27 + 15
Simplifying further, we get:
-3x > -12
Divide both sides of the inequality by -3, remembering to flip the sign:
x < 4 (after dividing by -3, flip the inequality sign)
2. Inequality 2:
Start with another inequality, for example, 2y - 1 > 5.
First, add 1 to both sides of the inequality:
2y - 1 + 1 > 5 + 1
2y > 6
Then, add 5 to both sides:
2y + 5 > 6 + 5
2y + 5 > 11
Next, multiply both sides by -3:
-3(2y + 5) < -3(11)
-6y - 15 < -33
This gives us the inequality: -6y < -33 + 15
Simplifying further, we get:
-6y < -18
Divide both sides of the inequality by -6, remembering to flip the sign:
y > 3 (after dividing by -6, flip the inequality sign)
So, the two inequalities that can be solved by adding 5 and multiplying by -3 are: x < 4 and y > 3.