-2/5x - 9 < 9/10
I understand how to do it without fractions but with fractions im completly lost. Can someone tell me how to do it? Do i subtract 9/10 - 9? If so then how would i do that?
I don't like fractions very much, so ...... multiply each term by 10
-2/5x - 9 < 9/10
-4x - 90 < 9
so much more civilized, don't you think?
btw, x > -99/4
Turn fractions into decimals.
2/5 = 0.4
9/10 = 0.9
https://www.mathsisfun.com/decimals-menu.html
with fractions, use a common denominator.
-2/5 x - 9 < 9/10
-4/10 x - 9 < 9/10
-4/10 x < 9 + 9/10
-4/10 x < 99/10
-x < 99/100 * 10/4
x > -99/40
Ok. So now i do 9 - 0.9 which is 8.1. Then i do -0.4x / -0.4 which is 1. Then i divide 8.1 by -0.4 which is -20.25. So i dont understand what my answer is. 1 or -20.25?
9/10 - 9 = 9/10 - 9/1 = 9/10 - 90/10 = -81/10 = -8 1/10 or -8.1
To solve inequalities involving fractions, you can follow these steps:
Step 1: Simplify both sides of the inequality by multiplying through by the least common denominator (LCD) of the fractions involved. In this case, the LCD is 10:
10 * (-2/5x - 9) < 10 * (9/10)
Simplifying:
-4x - 90 < 9
Step 2: Next, isolate the variable term (in this case, -4x) by moving all other terms to the opposite side of the inequality:
-4x < 9 + 90
Simplifying:
-4x < 99
Step 3: To solve for x, divide both sides of the inequality by the coefficient of x, which is -4. However, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign should be flipped:
x > 99 / -4
Simplifying:
x > -24.75
So, the solution to the inequality is x > -24.75.
Remember to keep track of the direction of the inequality sign throughout the steps, especially when flipping it due to multiplying or dividing by a negative number.