1/7 (3x+8)=1/2 (x-16) [[How do you work this problem out?]]?

Question

*answer please
*step-by-step

Answer 1

(use distributive property of multiplication)
1/7*3x + 1/7*8 = 1/2 *x - 1/2 * 16

(simplify)
3x/7 + 8/7 = x/2-8

Combine similar terms (terms with x will be in one side while all the known terms will be in one side)
3x/7 - x/2 = -8 - 8/7

( transform fractions to have common denominators)
3x/7 - 3.5x/7 = -56/7 - 8/7

Perform the operations
-0.5 x/7 = - 48/7

multiply both sides of the equation by 7
0.5x = - 48

divide both sides of the equation by - 0.5 leaving the variable alone in one side of the equation
x = 96 ___ final answer

Answer 2

There are lots of ways of doing this: Lucy has given you one way (but the answer is wrong !). Here is a method I liked:

Look at the denominators (7 and 2). Multiplying by 14 (the LCM) will get rid of all the fractions:

1/7 (3x + 8) = ½ (x - 16)
times by 14:
2(3x + 8) = 7(x - 16) {because 14*1/7 = 2 and 14*½ = 7}

6x + 16 = 7x - 112
16 + 112 = 7x - 6x

So x = 128

Answer 3

1/7 (3x + 8) = 1/2 (x - 16)
Multiply both sides by 14
2 (3x +8) = 7 (x -16)
6x + 16 = 7x - 112
112 + 16 = 7x - 6x
128 = x

Answer 4

X both sides by 14:-
2(3x + 8) = 7(x - 16)
6x + 16 = 7x - 112
x = 128

Answer 5

1/7(3x+8) = 1/2 (x-16)
by cross multiple
2(3x+8) = 7 ( x-16 )
6x + 16 = 7x - 112
x = 128

Answer 6

if given equation is
1/7(3x+8)=1/2(x-16)
3x/7+8/7=x/2-16/2
x/2-3x/7=8/7+16/2
-19x/14=128/14
-19x=128
x=-128/19

this is the required answer.

Answer 7

this is what I did for 7]. by means of aspects: enable u = ln(2x) and dv = a million/x^2 so as that du = a million/(2x) * (2) = a million/x and v = -a million/x. Then, int(u dv) = uv - int(v du) = ln(2x) * -a million/ x - int(-a million/x*a million/x) = -ln(2x) / x + int(a million/x^2) = -ln(2x) / x - a million/x + C this is what I did for (3). it truly is slightly unorthodox... int( (2x-a million) / (x + 3)^a million/2 ) = int( (2x+6) / (x + 3)^a million/2 ) - int( 7 / (x + 3)^a million/2 ) (considering that 6 + (-7) = -a million and breaking into 2 separate integrals) = 2*int( (x+3) / (x + 3)^a million/2 ) - int( 7 / (x + 3)^a million/2 ) (ingredient out 2) = 2*int( (x+3)^a million/2 ) - int( 7 / (x + 3)^a million/2 ) (simplify (x+3) / (x + 3)^a million/2 ) From here, that's in simple terms elementary u-substitution (enable u = x + 3 and combine. So to illustrate, int( (x+3)^a million/2) = 2/3*(x+3)^3/2 ). hence, we've: = 2*2/3*(x+3)^3/2 - 14(x+3)^a million/2 + C = 4/3*(x+3)^3/2 - 14(x+3)^a million/2 + C desire that facilitates.