Which of the following is the solution of the equation [tex]$3 x+4=19$[/tex]? Use substitution to identify the correct answer.
[tex]$x=5$[/tex]
[tex]$x=4$[/tex]
[tex]$x=6$[/tex]
[tex]$x=3$[/tex]
Answer (1)
Substitute each given value of x into the equation 3 x + 4 = 19 .
Check if the equation holds true for each value.
3 ( 5 ) + 4 = 19 , so x = 5 is a solution.
The solution to the equation is 5 .
Explanation
Understanding the Problem We are given the equation 3 x + 4 = 19 and four possible solutions: x = 5 , x = 4 , x = 6 , and x = 3 . We need to use substitution to find the correct solution. This means we will plug in each value of x into the equation and see which one makes the equation true.
Testing the Solutions Let's test each possible solution:
For x = 5 :
3 ( 5 ) + 4 = 15 + 4 = 19 Since 19 = 19 , x = 5 is a solution.
For x = 4 :
3 ( 4 ) + 4 = 12 + 4 = 16 Since 16 e q 19 , x = 4 is not a solution.
For x = 6 :
3 ( 6 ) + 4 = 18 + 4 = 22 Since 22 e q 19 , x = 6 is not a solution.
For x = 3 :
3 ( 3 ) + 4 = 9 + 4 = 13 Since 13 e q 19 , x = 3 is not a solution.
Finding the Solution Only x = 5 satisfies the equation 3 x + 4 = 19 . Therefore, the solution to the equation is x = 5 .
Examples
Imagine you're buying concert tickets online. Each ticket costs $3, and there's a $4 service fee for the entire order. If your total cost is $19, this problem helps you determine how many tickets you bought. By solving the equation 3 x + 4 = 19 , where x is the number of tickets, you find that you purchased 5 tickets. This kind of problem-solving is useful in budgeting, shopping, and many other everyday situations where you need to figure out quantities based on a total cost.
