Solve $2 x+2>10$
A. $x<6$
B. $x>6$
C. $x<4$
D. $x>4$
Answer (1)
Subtract 2 from both sides: 8"> 2 x > 8 .
Divide both sides by 2: 4"> x > 4 .
The solution to the inequality is 4"> x > 4 .
The final answer is 4}"> x > 4 .
Explanation
Understanding the Inequality We are given the inequality 10"> 2 x + 2 > 10 . Our goal is to isolate x on one side of the inequality to find the solution.
Subtracting 2 from Both Sides First, we subtract 2 from both sides of the inequality to get rid of the constant term on the left side:
10 - 2"> 2 x + 2 − 2 > 10 − 2
This simplifies to:
8"> 2 x > 8
Dividing by 2 Next, we divide both sides of the inequality by 2 to isolate x :
\frac{8}{2}"> 2 2 x > 2 8
This simplifies to:
4"> x > 4
Final Answer Therefore, the solution to the inequality 10"> 2 x + 2 > 10 is 4"> x > 4 . This corresponds to option D.
Examples
Imagine you're saving money for a new video game that costs $10. You already have $2 saved, and you earn $2 each week. The inequality 10"> 2 x + 2 > 10 helps you determine how many weeks ( x ) you need to save to have more than $10. Solving it shows you need to save for more than 4 weeks.
