   SEARCH HOME Math Central Quandaries & Queries  Question from maritza, a student: 5=3(x-2)= Maritza,

You didn't give us any instruction but I think you are to solve this equation for x. I am going to illustrate with a similar problem.

Solve the following equation for x: 7 = 4(3 - x)

The intent is to manipulate the equation and arrive with an equation of the form x = "some number". The manipulations must ensure that at every step the relationship remains an equality. The valid manipulations are

add the same amount to each side
subtract the same amount from each side
multiply each side by the same amount and
divide the same amount by the same amount as long as you don't divide by zero.

My equation is 7 = 4(3 - x). I am first going to use the distributive law to multiple (3 - x) by 4.

7 = 4(3 - x)
7 = 4 × 3 - 4 × x so
7 = 12 - 4x

I want the term involving x on the left side of the equation so add 4x to each side

7 = 12 - 4x
7 + 4x = 12 - 4x + 4x, which simplifies to
7 + 4x = 12

I don't want the 7 on the left side of the equation so subtract 7 from each side.

7 + 4x = 12
7 + 4x - 7 = 12 - 7, which simplifies to
4x = 5.

Finally divide both sides by 4 to get

4x = 5
4x/4 = 5/4 or
x = 5/4.

Now try your equation 5 = 3(x - 2).

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.