Solve the inequality for $x$.
$-13<4 x-5$
Simplify your answer as much as possible.
Answer (2)
Add 5 to both sides: − 13 + 5 < 4 x − 5 + 5 , which simplifies to − 8 < 4 x .
Divide both sides by 4: 4 − 8 < 4 4 x .
Simplify to find the solution: − 2 < x .
Express the solution: -2"> x > − 2 , so the final answer is -2}"> x > − 2 .
Explanation
Understanding the Inequality We are given the inequality − 13 < 4 x − 5 . Our goal is to isolate x on one side of the inequality to solve for its possible values.
Adding 5 to Both Sides To begin, we add 5 to both sides of the inequality to eliminate the constant term on the right side: − 13 + 5 < 4 x − 5 + 5
Simplifying the Inequality Simplifying both sides, we get: − 8 < 4 x
Dividing by 4 Next, we divide both sides by 4 to isolate x :
4 − 8 < 4 4 x
Simplifying for the Solution Simplifying again, we find: − 2 < x
Final Answer This inequality states that x is greater than -2. We can also write this as -2"> x > − 2 .
Examples
Imagine you're saving money, and you need to have more than $ -2 in your account. If each week you save 4 b u t s t a r tw i t ha -5 debt, this inequality helps you determine how many weeks you need to save to have more than $ -2. Understanding and solving inequalities is crucial for managing finances and planning future savings or investments.
To solve the inequality − 13 < 4 x − 5 , we isolate x by adding 5 to both sides and then dividing by 4, resulting in the solution -2"> x > − 2 .
;
