Can someone explain how to find the solution to the inequality. −2x − 14 > −4 + 3x Please show me step by step.
adding 4 ... −2x − 10 > 3x
adding 2x ... − 10 > 5x
dividing by 5 ... − 2 > x
−2x − 14 > −4 + 3x
Subtract 3x from both sides.
Add 14 to both sides.
-5x > 10
Divide both sides by -5.
But these things will change direction of the inequality:
Multiplying or dividing both sides by a negative number
Swapping left and right hand sides
x < -2
Thank you VERY much for helping me understand!
You're welcome.
Oh -- I forgot to attribute my source above --
https://www.mathsisfun.com/
To find the solution to the inequality -2x - 14 > -4 + 3x, you can follow these steps:
Step 1: Simplify the inequality by combining like terms. Add 2x to both sides of the inequality and add 14 to both sides:
-2x - 14 + 2x > -4 + 3x + 2x
-14 > -4 + 5x
Step 2: Simplify further by combining -4 and 5x:
-14 > 5x - 4
Step 3: To isolate the variable x, subtract -4 from both sides of the inequality:
-14 + 4 > 5x - 4 + 4
-10 > 5x
Step 4: Divide both sides of the inequality by 5 to solve for x. Remember to flip the inequality sign when dividing by a negative number:
-10/5 < 5x/5
-2 < x
So, the solution to the inequality is x > -2.