Solving Equations with variables on both sides. three times the sum of a number and 4 is 8 less than 1/2 the number. Write and solve an equation to...

Solve the following: Three times the sum of a
number and 4 is 8 less than 1/2 the number.

Note
the key words: times typically means multiply; sum means addition (Also notice the
multiplication is on the sum);is usually means equals;less than indicates subtraction;
1/2 the number means to multiply by 1/2 or divide by 2.

We
are looking for a number -- lets call it x.

Then we have
3(x+4)=1/2x-8. Read the sentence as you look at the equation and verbalize the algebra
operations.

Now the easy
part:

`3(x+4)=1/2x-8`

`6(x+4)=x-16`
Multiply both sides of the equation by 2 to clear the
fraction.

`6x+24=x-16` Use the distributive property to
eliminate the ()

`5x=-40` Subtract x from both
sides;subtract 24

`x=-8` Divide by
5

Check your answer: 3 times the sum of -8 and 4 is
3(-4)=-12

8 less than 1/2(-8) is
-4-8=-12.

Therefore the number we are seeking is
-8.