Solve the inequality. Using a verbal statement, in simplest terms, describe the solution of the inequality. Be sure to include the terms, "greater than", "greater than or equal to", "less than", or "less than or equal to".
-2x + 3 > 3(2x - 1)
The solution to the inequality -2x + 3 > 3(2x - 1) is x < 2/13.
In simpler terms, x is less than 2/13.
To solve the inequality -2x + 3 > 3(2x - 1), we need to simplify and isolate the variable x.
First, distribute 3 to both terms inside the parentheses:
-2x + 3 > 6x - 3
Next, bring like terms to one side of the inequality:
-2x - 6x > -3 - 3
-8x > -6
Now, divide both sides of the inequality by -8. Since we are dividing by a negative number, the direction of the inequality flips:
x < -6 / -8
x < 3/4
In simplest terms, the solution to the inequality -2x + 3 > 3(2x - 1) is x is less than 3/4.
To solve the inequality -2x + 3 > 3(2x - 1), we will simplify both sides of the inequality, isolate the variable x, and determine the range of values that satisfy the inequality.
First, we will simplify both sides of the inequality:
-2x + 3 > 6x - 3
Next, we will combine like terms on each side:
3 + 3 > 6x + 2x
6 > 8x
Now, we will isolate the variable x by dividing both sides of the inequality by 8:
6/8 > x
Reducing the fraction, we get:
3/4 > x
Therefore, the solution to the inequality -2x + 3 > 3(2x - 1) is x is less than or equal to 3/4.
In simple terms, x can be any value that is less than or equal to 3/4.