What's the equation for "ten times the sum of half a number and 6 is 8

Answers

Answer 1

Answer: 10(.5 + 6)=8

If you need me to explain, let me know.

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Answers

Answer:

(-6,9,-3)

Step-by-step explanation:

-3x -y +z=6

-3x-y+3z =0

x-3z =3

Multiply the second equation by -1

-1 *(-3x-y+3z) =0*-1

3x +y -3z =0

Add this to the first equation

-3x -y +z=6

3x +y -3z =0

----------------------

0 + 0 + -2z = 6

Divide by -2

-2z/-2 = 6/-2

z = 6/-2

z=-3

Take the third equation to find x

x-3z=3

x-3(-3) = 3

x+9=3

Subtract 9 from each side

x+9-9 =3-9

x=-6

Now we need to find y

3x +y -3z =0

3(-6) +y -3(-3) =0

-18 +y +9=0

-9+y =0

Add 9 to each side

-9+9+y = 0+9

y=9

(-6,9,-3)

$\left\{\begin{array}{ccc}-3x-y+z=6\n-3x-y+3z=0\nx-3z=3&|\text{add 3z to both sides}\end{array}\right\n\nx=3+3z\n\n\text{Substitute it to the first and the second equation:}\n\n\left\{\begin{array}{ccc}-3(3+3z)-y+z=6\n-3(3+3z)-y+3z=0\end{array}\right\n\n\text{use distributive property}\n\n\left\{\begin{array}{ccc}-9-9z-y+z=6&|\text{add 9 to both sides}\n-9-9z-y+3z=0&|\text{add 9 to both sides}\end{array}\right\n\n\text{combine like terms}$

$\left\{\begin{array}{ccc}-8z-y=15\n-6z-y=9&|\text{change the signs}\end{array}\right\n\n\underline{+\left\{\begin{array}{ccc}-8z-y=15\n6z+y=-9\end{array}\right}\qquad\text{add both sides of the equations}\n.\qquad-2z=6\qquad\text{divide both sides by (-2)}\n.\qquad\boxed{z=-3}\n\n\text{Put the value of z to the second equation:}\n\n6(-3)+y=-9\n-18+y=-9\qquad\text{add 18 to both sides}\n\boxed{y=9}\n\n\text{Put the value of z to the equation}\ x=3+3z:\n\nx=3+3(-3)\nx=3-9\n\boxed{x=-6}$

$Answer:\ \boxed{x=-6,\ y=9,\ z=-3\to(-6,\ 9,\ -3)}$

Albert used 3/8 of a half gallon of paint. What fraction of a gallon of paint did he use?