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 find the number.
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:
`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.