$3-4 x \geqslant x-7$
Answer (2)
The solution to the inequality 3 − 4 x ⩾ x − 7 is x ⩽ 2 , meaning x can be any number less than or equal to 2. We achieved this by isolating x through addition and division. This process ensures we understand how values relate under inequality constraints.
;
Add 4 x to both sides: 3 g e q s l an t 5 x − 7 .
Add 7 to both sides: 10 g e q s l an t 5 x .
Divide both sides by 5 : 2 g e q s l an t x .
The solution is x l e q s l an t 2 , which means x is less than or equal to 2. x l e q s l an t 2
Explanation
Understanding the Inequality We are given the inequality 3 − 4 xg e q s l an t x − 7 . Our goal is to isolate x on one side of the inequality to find the solution set.
Adding 4 x to Both Sides First, let's add 4 x to both sides of the inequality to get rid of the − 4 x term on the left side: 3 − 4 x + 4 xg e q s l an t x − 7 + 4 x This simplifies to: 3 g e q s l an t 5 x − 7
Adding 7 to Both Sides Next, we add 7 to both sides of the inequality to isolate the term with x on the right side: 3 + 7 g e q s l an t 5 x − 7 + 7 This simplifies to: 10 g e q s l an t 5 x
Dividing by 5 Now, we divide both sides of the inequality by 5 to solve for x :
5 10 g e q s l an t 5 5 x This simplifies to: 2 g e q s l an t x
Rewriting the Inequality This inequality can also be written as: x l e q s l an t 2
Final Answer Therefore, the solution to the inequality 3 − 4 xg e q s l an t x − 7 is x l e q s l an t 2 . This means that any value of x that is less than or equal to 2 will satisfy the original inequality.
Examples
Imagine you're managing a budget where you have $3 initially, and you spend $4 per item. You want to ensure that the total amount you have is always greater than or equal to the cost of buying one item plus a fixed cost of $7. Solving this inequality helps you determine the maximum number of items you can buy while staying within your budget. This type of problem is applicable in various resource allocation scenarios, helping to make informed decisions about spending and investments.
