# 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.

embizze | High School Teacher | (Level 1) Educator Emeritus

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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.