Answer:
2x = 6
Step-by-step explanation:
Simplify the following algebraic expressions.
- 6x + 5 + 12x -6
2(x - 9) + 6(-x + 2) + 4x
3x2 + 12 + 9x - 20 + 6x2 - x
(x + 2)(x + 4) + (x + 5)(-x - 1)
1.2(x - 9) - 2.3(x + 4)
(x2y)(xy2)
(-x2y2)(xy2)
Solution
Group like terms and simplify.
- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - 6)
= 6x - 1
Expand brackets.
2(x - 9) + 6(-x + 2) + 4x = 2x - 18 - 6x + 12 + 4x
Group like terms and simplify.
= (2x - 6x + 4x) + (- 18 + 12) = - 6
Group like terms and simplify.
3x2 + 12 + 9x - 20 + 6x2 - x
= (3x2 + 6x2) + (9x - x) + (12 - 20)
= 9x2 + 8x - 8
Expand brackets.
(x + 2)(x + 4) + (x + 5)(- x - 1)
= x2 + 4x + 2x + 8 - x2 - x - 5x - 5
Group like terms.
= (x2 - x2) + (4x + 2x - x - 5x) + (8 - 5)
= 3
Expand and group.
1.2(x - 9) - 2.3(x + 4)
= 1.2x - 10.8 - 2.3x - 9.2
= -1.1x - 20
Rewrite as follows.
(x2y)(xy2) = (x2 x)(y y2)
Use rules of exponential.
= x3 y3
Rewrite expression as follows.
(-x2y2)(xy2) = -(x2 x)( y2 y2)
Use rules of exponential.
= - x3 y4
Simplify the expressions.
(a b2)(a3 b) / (a2 b3)
(21 x5) / (3 x4)
(6 x4)(4 y2) / [ (3 x2)(16 y) ]
(4x - 12) / 4
(-5x - 10) / (x + 2)
(x2 - 4x - 12) / (x2 - 2 x - 24)
Solution
Use rules of exponential to simplify the numerator first.
(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)
Rewrite as follows.
(a4 / a2) (b3 / b3)
Use rule of quotient of exponentials to simplify.
= a2
Rewrite as follows.
(21 x5) / (3 x4) = (21 / 3)(x5 / x4)
Simplify.
= 7 x
(6 x4)(4 y2) / [ (3 x2)(16 y) ]
Multiply terms in numerator and denominator and simplify.
(6 x4)(4 y2) / [ (3 x2)(16 y) ] = (24 x4 y2) / (48 x2 y)
Rewrite as follows.
= (24 / 48)(x4 / x2)(y2 / y)
Simplify.
= (1 / 2) x2 y
Factor 4 out in the numerator.
(4x - 12) / 4 = 4(x - 3) / 4
Simplify.
= x - 3
Factor -5 out in the numerator.
(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)
Simplify.
= - 5
Factor numerator and denominator as follows.
(x2 - 4x - 12) / (x2 - 2x - 24) = [(x - 6)(x + 2)] / [(x - 6)(x + 4)]
Simplify.
= (x + 2) / (x + 4) , for all x not equal to 6
Solve for x the following linear equations.
2x = 6
