Question

How do you solve `8m + 5= 6m + 1`?

Answer 1

`m=-2`

Explanation:

I'll color like terms in red (variables with coefficients ♦) and blue (constants ♣). Your goal is to get one color on each side of the equals sign; that will help you simplify.

`\color(red)(8m)+\color(blue)(5)=\color(red)(6m)+\color(blue)(1)`

Subtract 6m from both sides:
`\color(red)(8m-6m)+\color(blue)(5)=\cancel(\color(red)(6m-6m))+\color(blue)(1)`
`\color(red)(2m)+\color(blue)(5)=\color(blue)(1)`

Subtract 5 from both sides:
`\color(red)(2m)+\cancel(\color(blue)(5-5))=\color(blue)(1-5)`
`\color(red)(2m)=\color(blue)(-4)`

Okay, now you can solve for the variable. Isolate it by dividing both sides by 2 (in green):
`(\cancel(2)m)/\cancel(\color(olive)(2))=-4/\color(olive)(2)`
`m=-2/1=-2`

♦ The numbers that are attached to variables are called "coefficients"
♣ Numbers that aren't attached to variables are usually referred to as "constants."