What is the solution to the equation 2(4 - 3x) + 5(2x - 3) = 20 - 5x? Options: A) x = -13 B) x = 5/4 C) x = 13/2 D) x = 3

To solve the equation 2 ( 4 − 3 x ) + 5 ( 2 x − 3 ) = 20 − 5 x , we need to follow these steps:

Distribute the constants in the equation:


For 2 ( 4 − 3 x ) , distribute 2: 2 × 4 − 2 × 3 x = 8 − 6 x .

For 5 ( 2 x − 3 ) , distribute 5: 5 × 2 x − 5 × 3 = 10 x − 15.



Substitute the results back into the equation: 8 − 6 x + 10 x − 15 = 20 − 5 x .

Combine like terms on the left side of the equation:



Combine − 6 x and 10 x :
− 6 x + 10 x = 4 x .

Combine 8 and − 15 :
8 − 15 = − 7. So the equation becomes: 4 x − 7 = 20 − 5 x .



Add 5 x to both sides to move all x terms to one side of the equation: 4 x + 5 x − 7 = 20. 9 x − 7 = 20.

Add 7 to both sides to solve for x : 9 x = 20 + 7. 9 x = 27.

Divide both sides by 9 to isolate x : x = 9 27 ​ . x = 3.


Thus, the solution to the equation is x = 3 .
The correct option is (\text{D}), x = 3."}

Answered by JessicaJessy | 2025-07-21