Solve the equation.3/4(2a − 6) + 1/2 = 2/5(3a + 20)

a = 40

Step-by-step explanation:

This is a multi-step equation using the distributive property and rational coefficents (fractions).  The first step is to complete the distributive property on both sides of the equation and multiply each term in the expression in parenthesis by the constant on the outside.  (3/4 x 2a) - (3/4 x 6) +1/2 = (2/5 x 3a) + (2/5 x 20).  When we multiply and simplify, we get 3/2a - 9/2 + 1/2 = 6/5a + 8.  Next step is to combine like terms:  3/2a  - 8/2 = 6/5a +8.  We then need to isolate the variable by using inverse operations:  3/10a = 12, then solve for 'a' by multiplying both sides by the reciprocal (10/3) to get a = 40.

it has changed from the width and the height.

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1