Solve the inequality for $x$.
$-3+2 x \leq-1$
Simplify your answer as much as possible.
Answer (2)
Add 3 to both sides: − 3 + 2 x + 3 ≤ − 1 + 3 , which simplifies to 2 x ≤ 2 .
Divide both sides by 2: 2 2 x ≤ 2 2 .
Simplify to find the solution: x ≤ 1 .
The solution to the inequality is x ≤ 1 .
Explanation
Understanding the Problem We are given the inequality − 3 + 2 x ≤ − 1 and our goal is to solve for x . This means we want to isolate x on one side of the inequality.
Adding 3 to Both Sides First, we add 3 to both sides of the inequality to get rid of the − 3 on the left side: − 3 + 2 x + 3 ≤ − 1 + 3
Simplifying the Inequality Simplifying both sides, we have: 2 x ≤ 2
Dividing by 2 Now, we divide both sides by 2 to isolate x : 2 2 x ≤ 2 2
Final Solution Simplifying again, we find the solution for x : x ≤ 1
Examples
Linear inequalities are used in everyday life to determine constraints. For example, if you have a budget of $50 and want to buy items that cost $5 each, the inequality 5 x ≤ 50 represents how many items ( x ) you can buy. Solving this inequality gives x ≤ 10 , meaning you can buy at most 10 items.
To solve the inequality -3 + 2x ≤ -1, we add 3 to both sides to get 2x ≤ 2, then divide by 2 resulting in x ≤ 1. Thus, the solution is x ≤ 1. The final answer is x ≤ 1 .
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