(2x-7)(3x+1)=(2x-5)(3x-1)solve for x
Answers
Answer:
Simplifying
(2x + -7)(3x + 1) = (2x + -5)(3x + 2)
Reorder the terms:
(-7 + 2x)(3x + 1) = (2x + -5)(3x + 2)
Reorder the terms:
(-7 + 2x)(1 + 3x) = (2x + -5)(3x + 2)
Multiply (-7 + 2x) * (1 + 3x)
(-7(1 + 3x) + 2x * (1 + 3x)) = (2x + -5)(3x + 2)
((1 * -7 + 3x * -7) + 2x * (1 + 3x)) = (2x + -5)(3x + 2)
((-7 + -21x) + 2x * (1 + 3x)) = (2x + -5)(3x + 2)
(-7 + -21x + (1 * 2x + 3x * 2x)) = (2x + -5)(3x + 2)
(-7 + -21x + (2x + 6x2)) = (2x + -5)(3x + 2)
Combine like terms: -21x + 2x = -19x
(-7 + -19x + 6x2) = (2x + -5)(3x + 2)
Reorder the terms:
-7 + -19x + 6x2 = (-5 + 2x)(3x + 2)
Reorder the terms:
-7 + -19x + 6x2 = (-5 + 2x)(2 + 3x)
Multiply (-5 + 2x) * (2 + 3x)
-7 + -19x + 6x2 = (-5(2 + 3x) + 2x * (2 + 3x))
-7 + -19x + 6x2 = ((2 * -5 + 3x * -5) + 2x * (2 + 3x))
-7 + -19x + 6x2 = ((-10 + -15x) + 2x * (2 + 3x))
-7 + -19x + 6x2 = (-10 + -15x + (2 * 2x + 3x * 2x))
-7 + -19x + 6x2 = (-10 + -15x + (4x + 6x2))
Combine like terms: -15x + 4x = -11x
-7 + -19x + 6x2 = (-10 + -11x + 6x2)
Add '-6x2' to each side of the equation.
-7 + -19x + 6x2 + -6x2 = -10 + -11x + 6x2 + -6x2
Combine like terms: 6x2 + -6x2 = 0
-7 + -19x + 0 = -10 + -11x + 6x2 + -6x2
-7 + -19x = -10 + -11x + 6x2 + -6x2
Combine like terms: 6x2 + -6x2 = 0
-7 + -19x = -10 + -11x + 0
-7 + -19x = -10 + -11x
Solving
-7 + -19x = -10 + -11x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '11x' to each side of the equation.
-7 + -19x + 11x = -10 + -11x + 11x
Combine like terms: -19x + 11x = -8x
-7 + -8x = -10 + -11x + 11x
Combine like terms: -11x + 11x = 0
-7 + -8x = -10 + 0
-7 + -8x = -10
Add '7' to each side of the equation.
-7 + 7 + -8x = -10 + 7
Combine like terms: -7 + 7 = 0
0 + -8x = -10 + 7
-8x = -10 + 7
Combine like terms: -10 + 7 = -3
-8x = -3
Divide each side by '-8'.
x = 0.375
Simplifying
x = 0.375
Concept:
Distributive law is also known as distributive property, this law relates the operations of multiplication and addition, and is represented as a (b + c) = ab + ac.
Given:
An equation (2x-7)(3x+1)=(2x-5)(3x-1).
Find:
The value of x for the equation (2x-7)(3x+1)=(2x-5)(3x-1).
Solution:
The given equation is,
( 2x−7 )( 3x+1 ) = ( 2x−5 )( 3x+2 )
Expanding the equation using distributive law,
6x² + 2x − 21x − 7 = 6x² + 4x − 15x −10
Canceling out the common terms and simplifying,
−19x −7 = − 11x −10
−19x + 11x = −10 + 7
−8x = −3
x = -3/-8 = 3/8
Hence, the value of x for the equation (2x-7)(3x+1)=(2x-5)(3x-1) is 3/8.
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