how do I solve using the multiplacation method
-2x>1/9
I guess that means that you multiply both sides by the reciprocal of the coefficient thusly:
-2x * 1/-2 < 1/9 * 1/-2
x < -1/18
Have you wondered why multiplying by a negative flips the direction of the inequality? It's just a shorthand way of moving items to the other side.
-2x < 4
Now suppose you want +2x: Just add 2x to each side
-2x + 2x < 4 + 2x
0 < 4 + 2x
Now subtract 4 from both sides:
-4 < 2x
But that's the same as
2x > -4
which is what you get by multiplying by -1 and swapping direction.
To solve the inequality -2x > 1/9 using the multiplication method, you need to follow these steps:
Step 1: Isolate the variable. Since the variable (-2x) is on the left side of the inequality, you need to move it to the right side. To do this, you can divide both sides of the inequality by -2, but since you're dividing by a negative number, remember to reverse the inequality sign. This step gives you:
x < (1/9) / -2
Step 2: Simplify the right side of the inequality. To divide 1/9 by -2, you can multiply the numerator (1) by the reciprocal of the denominator (9). The reciprocal of -2 is -1/2. So, the right side becomes:
x < (1/9) * (-1/2)
Simplifying the multiplication gives you:
x < -1/18
Therefore, the solution to the inequality -2x > 1/9 is x < -1/18.