Which equations have the same value of [tex]$x$[/tex] as [tex]$\frac{3}{5}(30 x-15)=72$[/tex]? Select three options.
[tex]$18 x-15=72$[/tex]
[tex]$50 x-25=72$[/tex]
[tex]$18 x-9=72$[/tex]
[tex]$3(6 x-3)=72$[/tex]
[tex]$x=4.5$[/tex]
Answer (1)
Solve the given equation 5 3 ( 30 x − 15 ) = 72 and find that x = 4.5 .
Check each option by substituting x = 4.5 into the equation.
Identify the equations that hold true when x = 4.5 .
The equations with the same solution are 18 x − 9 = 72 , 3 ( 6 x − 3 ) = 72 , and x = 4.5 .
Explanation
Understanding the Problem We are given the equation 5 3 ( 30 x − 15 ) = 72 and asked to find three equations from the given options that have the same solution.
Solving the Original Equation First, let's solve the given equation for x :
5 3 ( 30 x − 15 ) = 72
3 ( 6 x − 3 ) = 72
18 x − 9 = 72
18 x = 72 + 9
18 x = 81
x = 18 81 = 2 9 = 4.5
Checking the Options Now, we will check each of the given options to see if they have the same solution x = 4.5 .
Option 1: 18 x − 15 = 72 18 x = 72 + 15
18 x = 87
x = 18 87 = 6 29 ≈ 4.833 = 4.5
So, Option 1 is not a correct answer.
Option 2: 50 x − 25 = 72 50 x = 72 + 25
50 x = 97
x = 50 97 = 1.94 = 4.5
So, Option 2 is not a correct answer.
Option 3: 18 x − 9 = 72 18 x = 72 + 9
18 x = 81
x = 18 81 = 2 9 = 4.5
So, Option 3 is a correct answer.
Option 4: 3 ( 6 x − 3 ) = 72 18 x − 9 = 72
18 x = 72 + 9
18 x = 81
x = 18 81 = 2 9 = 4.5
So, Option 4 is a correct answer.
Option 5: x = 4.5 So, Option 5 is a correct answer.
Final Answer The equations with the same solution as the given equation are: 18 x − 9 = 72 , 3 ( 6 x − 3 ) = 72 , and x = 4.5 .
Examples
Imagine you're baking a cake and need to adjust the recipe. If the original recipe, represented by an equation, makes a cake that's too large, you need to find alternative recipes (equations) that yield the same result (cake size) but with different ingredient quantities. Solving and comparing equations helps you find the right adjustments to get the desired outcome without changing the final product.
