Solve for $x$
$3 x+3-x+(-7)>6$
A) $x<5$
B) $x>5$
C) $x>(-5)$
D) $x>2.5$
Answer (2)
Combine like terms: 6"> 3 x − x + 3 − 7 > 6 becomes 6"> 2 x − 4 > 6 .
Add 4 to both sides: 10"> 2 x > 10 .
Divide by 2: 5"> x > 5 .
The solution is 5}"> x > 5 .
Explanation
Understanding the Problem We are given the inequality 6"> 3 x + 3 − x + ( − 7 ) > 6 . Our goal is to solve for x .
Simplifying the Inequality First, we simplify the left side of the inequality by combining like terms. We have 3 x − x = 2 x and 3 − 7 = − 4 . So the inequality becomes 6"> 2 x − 4 > 6 .
Isolating the x term Next, we want to isolate the term with x . To do this, we add 4 to both sides of the inequality: 6 + 4"> 2 x − 4 + 4 > 6 + 4 , which simplifies to 10"> 2 x > 10 .
Solving for x Now, we divide both sides of the inequality by 2 to solve for x : \frac{10}{2}"> 2 2 x > 2 10 , which simplifies to 5"> x > 5 .
Final Answer Therefore, the solution to the inequality is 5"> x > 5 . Comparing this to the given options, we see that option B is the correct answer.
Examples
Imagine you're saving money, and you want to know how many weeks it will take to have more than $6 in your account. If you start with $3 and save an additional amount each week, represented by 'x', but also have a fixed expense of $7, this inequality helps you determine the number of weeks needed to have more than $6. Understanding and solving such inequalities is crucial for financial planning and budgeting.
After simplifying the inequality, we find that 5"> x > 5 . Therefore, the answer is option B. This means that any value of x greater than 5 satisfies the inequality.
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