Solving General Equations

Deal with parenthesis The first step is distributing, then it is solved like any other two-step equation. Example
`4(2x−6)=16`Distribute `4` through parenthesis
`8x−24=16 `Focus on the subtraction first
`8x−24color(red)(+24)=16color(red)(+24) `Add `24` to both sides
`8x=40 `Now focus on the multiply by `8`
`(8x)/color(red)(8)=40/color(red)(8)`Divide both sides by `8`
`x=5 `Solution!
Combine like terms Often after we distribute there will be some like terms on one side of the equation. Next Example shows distributing to clear the parenthesis and then combining like terms next. Once we have done this, our next example solves just like any other two-step equation. Example
`3(2x−4)+9=15`Distribute the `3` through the parenthesis
`6x−12+9=15 `Combine like terms,`−12+9`
`6x−3=15 `Focus on the subtraction first
`6x−3color(red)(+3)=15 color(red)(+3)`Add 3 to both sides
`6x=18 `Now focus on multiply by 6
`(6x)/color(red)(6)=18/color(red)(6) `Divide both sides by 6
`x = 3 `Solution!
Variable on both sides A second type of problem that becomes a two-step equation after a bit of work is one where we see the variable on both sides. This is shown in the following example. Example
`4x− 6 = 2x+ 10`Notice the variable on both sides
`4xcolor(red)(-2x) − 6 = 2xcolor(red)(-2x) + 10`Subtract `2x` from both sides
`2x − 6 = 10`Focus on the subtraction first
`2x − 6color(red)(+6) = 10color(red)(+6) `Add `6` to both sides
`2x = 16`Focus on the multiplication by `2`
`(2x)/color(red)(2) = 16/color(red)(2) `Divide both sides by `2`
`x=8 `Solution!