Solve for x.

$5x + 54 \geq 74$

Subtract 54 from both sides: 5 x + 54 − 54 ≥ 74 − 54 , which simplifies to 5 x ≥ 20 .
Divide both sides by 5: 5 5 x ​ ≥ 5 20 ​ .
Simplify to find the solution: x ≥ 4 .
The solution to the inequality is x ≥ 4 ​ .

Explanation

Understanding the Inequality We are given the inequality 5 x + 54 ≥ 74 . Our goal is to isolate x on one side of the inequality to find the solution.

Subtracting 54 from Both Sides First, we subtract 54 from both sides of the inequality to start isolating the term with x : 5 x + 54 − 54 ≥ 74 − 54

Simplifying the Inequality This simplifies to: 5 x ≥ 20

Dividing by 5 Next, we divide both sides of the inequality by 5 to solve for x :
5 5 x ​ ≥ 5 20 ​

Final Solution This simplifies to: x ≥ 4 Therefore, the solution to the inequality is x ≥ 4 . This means that x can be any number greater than or equal to 4.


Examples
Imagine you are saving money for a new bicycle that costs $74. You already have $54 saved, and you plan to save an additional $5 each week. The inequality 5 x + 54 ≥ 74 helps you determine the minimum number of weeks ( x ) you need to save to afford the bicycle. Solving this inequality tells you that you need to save for at least 4 weeks to have enough money.

Answered by GinnyAnswer | 2025-07-08

To solve the inequality 5 x + 54 ≥ 74 , we isolate x by subtracting 54 and dividing by 5, leading to the solution x ≥ 4 . This indicates x can be any value greater than or equal to 4. Hence, you need to save at least 4 weeks to reach your financial goal.
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Answered by Anonymous | 2025-07-28