Solve the equation [tex]$3(x-7)=42$[/tex]
Answer (1)
Distribute the constant: 3 ( x − 7 ) = 3 x − 21 .
Add 21 to both sides: 3 x = 42 + 21 = 63 .
Divide by 3: x = 3 63 = 21 .
The solution is 21 .
Explanation
Understanding the Problem We are given the equation 3 ( x − 7 ) = 42 and asked to solve for x . We need to isolate x by performing algebraic operations on both sides of the equation.
Distributing the Constant First, distribute the 3 on the left side of the equation: 3 ( x − 7 ) = 3 x − 3 ( 7 ) = 3 x − 21
So the equation becomes: 3 x − 21 = 42
Isolating the x Term Next, add 21 to both sides of the equation to isolate the term with x :
3 x − 21 + 21 = 42 + 21 3 x = 63
Solving for x Now, divide both sides of the equation by 3 to solve for x :
3 3 x = 3 63 x = 21
Final Answer Therefore, the solution to the equation 3 ( x − 7 ) = 42 is x = 21 . Comparing this to the given options, we see that the correct answer is C) 21.
Examples
Imagine you're planning a road trip with friends. You need to split the total cost of gas equally. If the total gas cost is represented by the equation 3 ( x − 7 ) = 42 , where x is the amount each person pays, solving this equation helps you determine the exact amount each friend needs to contribute. This ensures a fair distribution of expenses, making the trip enjoyable for everyone. Understanding how to solve such equations is useful in everyday scenarios where costs need to be divided or resources allocated equally.
