Solve the inequality step by step. Explain, please, each step! -7-3x<5x+29
First, we have to subtract 5x, both sides of the inequality:
Now, we'll keep the unknown to the left side of the inequality and we'll multiply the inequality, both sides, by -1. Because of the negative value, the sign of the inequality will be changed, after multiplying.
Now, we'll subtract 7, both sides of the inequality, and we'll get:
Now, we'll divide the inequality by 8:
The solution of the inequality consists in all x values from the interval (-9/2, inf).
We solve inquallities by (i) adding or subtracting equals which does not change the inequality, Or by multiplying by equal and postive values which does not change the inequality. We do these operaations one by one (or several operations) till all x's (unknowns ) one side of our convenience and the numbers (or knowns ) are on the other side.
We would like to take x's right and numbers to left,. With this we as below
-7-3x < 5x+29 is the given equation. Or
-7-3x -29 < 5x+29-29 . From both sides 29 is subtracted.Now simplify both sides.
-3x-36 < 5x. Or
-3x-36 +3x < 5x+3x. Subtracted 3x from both sides.Simplify:
-36 < 8x. Or
-36/8 < 8x/8. We divided by 2 which is positive and so the inequality sign remains unchanged. (Mind that if you multiply both sides by equals which are negative , then the ineqality reverses!). Therefore,
-4.5 < x . Or
x > -4.5