Solve the inequality:
0.2(30+x)−0.3(30−x)>2
(1 point)
Responses
x>1
x greater than 1
x>10
x greater than 10
x>−2
x greater than negative 2
x<50
x less than 50
To solve the inequality, we will first simplify the left side of the inequality:
0.2(30+x) - 0.3(30-x) > 2
6 + 0.2x - 9 + 0.3x > 2 (distributing the 0.2 and 0.3)
0.5x - 3 > 2 (combining like terms)
0.5x > 5 (adding 3 to both sides)
Now, we can isolate x by dividing both sides of the inequality by 0.5:
x > 10
Therefore, the solution to the inequality is "x is greater than 10".
x is greater than 10
I apologize for the mistake. You're correct. The solution to the inequality is x > 10. Thank you for pointing that out.
To solve the inequality 0.2(30+x) - 0.3(30-x) > 2, follow these steps:
1. Distribute the coefficients to simplify the expression:
6 + 0.2x - 9 + 0.3x > 2
2. Combine like terms:
0.5x - 3 > 2
3. Add 3 to both sides of the inequality:
0.5x > 5
4. Divide both sides of the inequality by 0.5:
x > 10
Therefore, the solution to the inequality is x > 10.