Solve: 2(2-x)<-3x-2...please help me solve this and show me how you get the answer...
2(2-x)<-3x-2
Just start working with the equation as if the < sign was an = sign
4 - 2x < -3x -2
4 + x < -2
x < -6
Thank You
To solve the inequality 2(2 - x) < -3x - 2, we'll first simplify the expression, then isolate the variable x.
1. Distribute the 2 on the left side:
2(2 - x) < -3x - 2
4 - 2x < -3x - 2
2. Move all terms involving x to one side:
-2x + 3x < -2 - 4
x < -6
Thus, the solution to the inequality is x < -6.
To understand the steps better, let's break down how we arrived at the solution:
Step 1: Distributive Property
We distribute the 2 to both terms inside the parentheses:
4 - 2x < -3x - 2
Step 2: Combine like terms
On the left side, we have a positive 4 and a negative 2x. On the right side, we have a negative 3x and a negative 2. To simplify, we group like terms together:
-2x + 3x < -2 - 4
Step 3: Combine the x terms
Combine the x terms on the left side of the inequality:
-2x + 3x = x
x < -2 - 4
Step 4: Simplify the remaining terms
Simplify the terms on the right side of the inequality:
x < -6