-Write an algebraic expression and solve the equation for: Eight less than four times a number is the same as eight times the sum of the number and two. What is the number?
-If 18 is decreased by the sum of a number and 6, the result is 4 less than 3 times the number. Find the number.
-A triangle has a perimeter of 29 cm. The sides have lengths, in centimeters, that are consecutive odd integers. What is the length of the longest side?
-1/3 ( x - 2 ) = x + 4
-15 - 1/8 d = -1
2007-01-27 05:34:32 · 4 answers · asked by sillentfeline 1 in Science & Mathematics ➔ Mathematics
1. 4x - 8 = 8(x+2)
First: eliminate parenthesis > use distribution - multiply the outer term with the terms in parenthesis...
4x - 8 = 8(x) + 8(2)
4x - 8 = 8x + 16
Sec: add "8" to both sides (when you move a variable to the opposite side, always use the opposite sign )...
4x - 8 + 8 = 8x + 16 + 8
4x = 8x + 24
Third: subtract "8x" from both sides...
4x - 8x = 8x - 8x + 24
- 4x = 24
*Isolate "x" on one side > divide both terms by "-4"...
(-4x)/-4 = 24/-4
x = -6
2. Expression > x + 6 - 18 = 3x - 4
First: combine "like" terms...
x - 12 = 3x - 4
Sec: add "12" to both sides...
x - 12 + 12 = 3x - 4 + 12
x = 3x + 8
Third: subtract "3x" from both sides...
x - 3x = 3x - 3x + 8
-2x = 8
*isolate "x" on one side > divide both terms by "-2"...
(-2x)/-2 = 8/-2
x = - 4
4. -1/3(x - 2) = x + 4
First: use distribution-multiply the outer term with the terms in parenthesis....
(-1/3)(x) - (1/3)(- 2) = x + 4
-1x/3 - (-2/3) = x + 4
-1x/3 + 2/3 = x + 4
Sec: eliminate fractions-multiply the denominator by everything...
(3)(-1x/3) + (3)(2/3) = (3)(x) + (3)(4)
*Cross cancel "like" terms & combine the remaining terms...
- x + 2 = 3x + 12
Third: subtract "2" from both sides...
- x + 2 - 2 = 3x + 12 - 2
- x = 3x + 10
*Subtract "3x" from both sides...
- x - 3x = 3x - 3x + 10
- 4x = 10
Fourth: isolate "x" on one side > divide both sides by "-4"...
(- 4x)/-4 = 10/-4
x = -10/4
x = -5/2
5. -15 - 1/8d = -1
First: eliminate the fraction - multiply the denominator by everything...
(8d)(-15) - (8d)(1/8d) = (8d)(-1)
Sec: cross cancel "like" terms & combine the remaining terms...
- 12d - 1 = - 8d
Third: add "12d" to both sides...
- 12d + 12d - 1 = - 8d + 12d
- 1 = 4d
Fourth: isolate "d" on one side > divide both terms by "4"...
-1/4 = 4d/4
-1/4 = d
d = -1/4
2007-01-27 05:54:14 · answer #1 · answered by ♪♥Annie♥♪ 6 · 0⤊ 1⤋
Let x = the number
4x-8 = 8(x+2)
4x-8 =8x+16
4x-8x = 16+8
-4x = 24
x = -6
Let x = the number
18-(x+6) = 3x-4
18-x-6 = 3x-4
-x-3x= -4-18 +6
-4x = -16
x=4
Let the three sides be 2x+1, 2x +3 and 2x+5
Their sum = 6x+9 = 29
6x = 20
x+3 2/3 So largest number is 2(11/3) + 5 = 22/3+5 = 12 1/3 which is not an integer, so there is no solution to this problem.
There are no consecutive odd integers that add up to 29.
-1/3 ( x - 2 ) = x + 4
-x/3 + 2/3 = x + 4
-x/3 - x = 4 - 2/3
-4x/3 = 10/3
-4x=10
x = - 10/4 = - 2.5
-15 - 1/8 d = -1
-d/8= -1 + 15 = 14
-d = 14*8 = 112
d = -112
2007-01-27 06:02:36 · answer #2 · answered by ironduke8159 7 · 0⤊ 1⤋
4n-8 = 8(n+2) ; n = -12
18-(n+6) = 3n-4 ; n=4
No solvable; The sum of three consecutive odd intergers must always be divisible by 3.
Are you asking Yahoo to do your homework?
2007-01-27 05:47:05 · answer #3 · answered by Mary Anne 2 · 0⤊ 1⤋
4x-8 = 8(x+2)
4x-8 = 8x+16
4x = 8x+24
-4x=24
x=(-6)
2007-01-27 05:45:27 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Ok the second question the answer is 5.
2007-01-27 05:40:56 · answer #5 · answered by Anonymous · 0⤊ 1⤋