Respuesta :
The equation computed shows that the correct options are A, B, and D.
How to illustrate the information?
1) The equation we want to rewrite is;
³/₅x + ²/₃ + x = ¹/₂ – ¹/₅x
(³/₅ + 1)x + ²/₃ = ¹/₂ – ¹/₅x
⁸/₅x + ²/₃ = ¹/₂ – ¹/₅x
This corresponds with the solution in Option A
2) ³/₅x + ²/₃ + x = ¹/₂ – ¹/₅x
Let us use multiplication property of equality which states that if we multiply both sides of an equation by the same quantity, then both sides remain equal.
Let's get rid of the denominators by multiplying each term by the LCM of the denominators. LCM of 2,3,5 is 30. Thus;
30(³/₅x) + 30(²/₃) + 30x = 30(¹/₂) - 30(¹/₅x)
Simplifying gives;
18x + 20 + 30x = 15 - 6x
This solution corresponds with that in option B
3) We will make use of additive property of equality which states that when we add the same number to both sides of an equation, then both sides remain equal.
Let's add 6x to both sides of 18x + 20 + 30x = 15 - 6x;
18x + 20 + 30x + 6x = 15 - 6x + 6x
⇒ 24x + 30 + 20 = 15
Using subtractive property of equality, let us subtract 20 from both sides to get;
24x + 30 + 20 - 20 = 15 - 20
This corresponds with the solution in Option D.
Complete question:
Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all that apply.
a. 8/5x+2/3=1/2-1/5x
b. 18x + 20 + 30x = 15 – 6x
c. 18x + 20 + x = 15 – 6x
d. 24x + 30x = –5
e. 12x + 30x = –5
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