Complete each step to solve the inequality for x. First, get the x-term by itself on one side of the inequality. How will you remove the "+7"? [tex]4 x+7\ \textgreater \ -17[/tex]
Answer (2)
To isolate the x-term in the inequality -17"> 4 x + 7 > − 17 , subtract 7 from both sides, resulting in -24"> 4 x > − 24 . By doing this, we remove the constant and prepare to solve for x . This process is crucial in solving inequalities and understanding how to maintain balance in equations.
;
To isolate the x-term, subtract 7 from both sides of the inequality.
This gives -17 - 7"> 4 x + 7 − 7 > − 17 − 7 .
Simplifying, we get -24"> 4 x > − 24 .
Therefore, to remove the '+7', you subtract 7 from both sides.
Explanation
Removing the Constant Term To isolate the x term in the inequality -17"> 4 x + 7 > − 17 , we need to remove the + 7 from the left side. We can do this by applying the inverse operation, which is subtraction.
Subtracting 7 from Both Sides Subtracting 7 from both sides of the inequality maintains the balance and isolates the term with x :
-17 - 7"> 4 x + 7 − 7 > − 17 − 7
This simplifies to:
-24"> 4 x > − 24
Examples
Imagine you're trying to figure out how many apples you need to sell to make a certain amount of money. If each apple costs $4 and you already have a debt of $7, this inequality helps you determine how many apples you need to sell to have more than $17 after paying off your debt. Understanding and solving inequalities is crucial in managing finances and making informed decisions about sales and profits.
