Solve the equation [tex]$9 x-2=16$[/tex]
A) [tex]$32 / 9$[/tex]
B) 2
C) [tex]$14 / 9$[/tex]
D) 4
Answer (2)
Add 2 to both sides of the equation: 9 x − 2 + 2 = 16 + 2 , which simplifies to 9 x = 18 .
Divide both sides by 9: 9 9 x = 9 18 .
Simplify to find the value of x : x = 2 .
The solution to the equation is 2 .
Explanation
Understanding the Problem We are given the equation 9 x − 2 = 16 and asked to solve for x . This is a linear equation, and we can solve it by isolating x on one side of the equation.
Adding 2 to Both Sides First, we add 2 to both sides of the equation to isolate the term with x : 9 x − 2 + 2 = 16 + 2
Simplifying the Equation This simplifies to: 9 x = 18
Dividing by 9 Next, we divide both sides of the equation by 9 to solve for x :
9 9 x = 9 18
Final Answer This simplifies to: x = 2 Therefore, the solution to the equation 9 x − 2 = 16 is x = 2 .
Examples
Linear equations like this one are used in everyday life to solve various problems. For example, if you want to buy a certain number of items that each cost the same amount, and you have a coupon that reduces the total cost, you can use a linear equation to determine how many items you can buy. Suppose you have a coupon for $2 off your entire purchase, and you want to buy items that cost $9 each. If you have $16 to spend, the equation 9 x − 2 = 16 can help you determine that you can buy 2 items.
To solve the equation 9 x − 2 = 16 , add 2 to both sides to get 9 x = 18 , then divide by 9, resulting in x = 2 . The correct answer is option B) 2.
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