Find the solution of [tex]7 x=35[/tex], and verify your solution using substitution.
A) [tex]x=6 ; 7(6)=35,35=35[/tex]
B) [tex]x=-5 ; 7(-5)=35,-35=-35[/tex]
C) [tex]x=5 ; 7(5)=35,35=35[/tex]
D) [tex]x=245 ; 7(35)=245,245=245[/tex]
Answer (2)
Divide both sides of the equation 7 x = 35 by 7 to isolate x .
Simplify the equation to find x = 5 .
Substitute x = 5 back into the original equation: 7 ( 5 ) = 35 .
Verify that the equation holds true, confirming the solution: x = 5 .
Explanation
Understanding the Problem We are given the equation 7 x = 35 and asked to find the solution and verify it using substitution.
Isolating x To solve for x , we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 7: 7 7 x = 7 35
Finding the Solution Simplifying the equation, we get: x = 5
Verifying the Solution Now, we need to verify our solution by substituting x = 5 back into the original equation: 7 ( 5 ) = 35
Checking the Solution Since 7 ( 5 ) = 35 , the left-hand side (LHS) equals the right-hand side (RHS), so our solution is correct.
Final Answer Therefore, the solution to the equation 7 x = 35 is x = 5 .
Examples
Imagine you're buying multiple items of the same price. If you know that 7 identical items cost $35, this problem helps you determine the price of a single item. This type of problem is useful in everyday situations such as calculating unit prices while shopping, determining the cost of individual components in a project, or figuring out how much of an ingredient to use in a recipe based on the total amount needed.
The solution to the equation 7 x = 35 is x = 5 , which can be verified by substituting back into the equation. The left-hand side equals the right-hand side, confirming the solution is correct.
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