I need help please!
What is the solution set?
−2.8x+5.6<8.4
−2.8x+5.6 < 8.4
-2.8x < 2.8
x > -1
To find the solution set of the inequality −2.8x + 5.6 < 8.4, we will follow these steps:
Step 1: Simplify the equation.
Start by subtracting 5.6 from both sides of the inequality:
−2.8x + 5.6 - 5.6 < 8.4 - 5.6
Simplifying the equation gives:
−2.8x < 2.8
Step 2: Divide both sides of the inequality by −2.8.
Since we need to get x alone, divide both sides of the inequality by −2.8 (the coefficient of x). Note that when dividing by a negative number, the inequality sign will flip.
−2.8x / −2.8 > 2.8 / −2.8
Simplifying the equation gives:
x > -1
Step 3: Express the solution set.
The solution to the inequality x > -1 is represented by the set of all numbers that are greater than -1. This can be expressed as:
{x | x > -1}
In conclusion, the solution set to the inequality −2.8x + 5.6 < 8.4 is {x | x > -1}.