Solve $58-10 x \leq 20+9 x$
A. $x \leq-2$
B. $x \geq 2$
C. $x \leq 2$
D. $x \geq-2$
Answer (1)
Add 10 x to both sides: 58 ≤ 20 + 19 x .
Subtract 20 from both sides: 38 ≤ 19 x .
Divide both sides by 19: 2 ≤ x .
Rewrite the inequality: xg e q 2 . The final answer is xg e q 2 .
Explanation
Understanding the Inequality We are given the inequality 58 − 10 x ≤ 20 + 9 x . Our goal is to isolate x on one side of the inequality to find the solution.
Adding 10 x to Both Sides First, we want to group the terms with x on one side and the constants on the other. We can add 10 x to both sides of the inequality to get: 58 − 10 x + 10 x ≤ 20 + 9 x + 10 x
58 ≤ 20 + 19 x
Subtracting 20 from Both Sides Next, we subtract 20 from both sides to isolate the term with x :
58 − 20 ≤ 20 + 19 x − 20 38 ≤ 19 x
Dividing by 19 Now, we divide both sides by 19 to solve for x :
19 38 ≤ 19 19 x 2 ≤ x
Final Answer This inequality can be rewritten as xg e q 2 . Therefore, the solution to the inequality is x is greater than or equal to 2.
Examples
Imagine you're saving money. You start with $58 and spend $10 each week. Your friend starts with $20 and saves $9 each week. The inequality helps determine after how many weeks your friend will have more money than you. This type of problem is useful in budgeting, comparing costs, and planning investments.
