a) 2 (5x-3) = 24
= 10x -6 = 24
= 10x = 24+6
= 10x = 30
= x= 30/10
b) 5 (2x+1) = 50
= 10x+5=50
= 10x = 50-5
= 10x = 45
= x = 45/10
c) (3x+4)/2=9.5
= (3x+4)/2=95/10
( On cross multiplication )
= 10(3x+4) = 2×95
= 30x+40=190
= 30x=190-40
= 30x=150
= x=150/30
(on simplification)
d) (7+2x)/3=5
(On cross multiplication)
= 1(7+2x)=5(3)
= 7+2x=15
= 2x=15-7
= 2x=8
= x=8/2
(on dividing)
Answer:
Step-by-step explanation:
yo yo yo
= bo obobo ooboob
Answer: True
Explanation:
According to the rational zeros theorem, if x=a is a zero of the function f(x), then f(a) = 0.
Given: f(x) = x⁴ + x³ - 11x² - 9x + 18
From the calculator, obtain
f(5) = 448
f(4) = 126
f(3) = 0
f(2) = -20
f(1) = 0
f(0) = 18
f(-1) = 16
f(-2) = 0
f(-3) = 0
The polynomial is of degree 4, so it has at most 4 real zeros.
From the calculations, we found all 4 zeros as x = -3, -2, 1, and 3.
Therefore
f(x) = (x+3)(x+2)(x-1)(x-3).
For x>3, f(x)increases rapidly. Therefore there are no zeros for x>3.
The statement that x=5 is an upper bound for the zeros of f(x) is true.
Answer:
x=12
Step-by-step explanation:
Simplifying
30 + 4x + 2 = 8 + 6x
Reorder the terms:
30 + 2 + 4x = 8 + 6x
Combine like terms: 30 + 2 = 32
32 + 4x = 8 + 6x
Solving
32 + 4x = 8 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
32 + 4x + -6x = 8 + 6x + -6x
Combine like terms: 4x + -6x = -2x
32 + -2x = 8 + 6x + -6x
Combine like terms: 6x + -6x = 0
32 + -2x = 8 + 0
32 + -2x = 8
Add '-32' to each side of the equation.
32 + -32 + -2x = 8 + -32
Combine like terms: 32 + -32 = 0
0 + -2x = 8 + -32
-2x = 8 + -32
Combine like terms: 8 + -32 = -24
-2x = -24
Divide each side by '-2'.
x = 12
Simplifying
x = 12
