Print-friendly page

Solving Multi-Step Linear Equations (page 2 of 3)

Sections: One-step equations, Multi-step equations, "No solution" and "all x" equations

Most linear equations require more than one step for their solution. For instance:

• Solve 7x + 2 = –54

I need to undo the "times seven" and the "plus two". There is no rule about which "undo" I should do first. However, if I first divide through by 7, I'm going to have fractions. Personally, I prefer to avoid fractions if possible, so I almost always do the plus/minus before the times/divide:

Then the solution is x = –8. 

By the way, formatting your homework and showing your work in the manner I have done is fairly universally acceptable.  Your teacher should be happy to see your homework looking like these examples. It is also a good idea to clearly rewrite your final answer at the end of each problem. Don't expect your grader to dig through your work to figure out what you meant the answer to be.

• Solve –5x – 7 = 108

Then the solution is  x = –23.

• Solve 3x – 9 = 33 Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

Then the solution is  x = 14.

• Solve 5x + 7x = 72

First, I need to combine like terms on the left; then I can solve:

Then the solution is  x = 6.

• Solve 4x – 6 = 6x

I need to move all the x's over to one side or the other. To avoid negative coefficients on my variables, I usually move the smaller x; in this case, I'll subtract the 4x over to the other side:

Then the solution is x = –3.

In the above exercise, note that it is perfectly okay to have the "x=" be on the right. The variable is not required to be on the left; we're just used to seeing it there. It's alright if your solution works out with the variable on the right. However, I've heard of some instructors who insist that, in the final answer, the variable be placed on the left-hand side. If you're in doubt about your instructor's preferred formatting, ask.

• Solve 8x – 1 = 23 – 4x

Then the solution is  x = 2.

• Solve 5 + 4x – 7 = 4x – 2 – x

Before I can solve, I need to combine like terms:

Then the solution is x = 0.

In the above problem, note that it is perfectly okay for x to be zero. Zero is a valid solution. Do not say "no solution"; this equation does indeed have a solution, the solution of x = 0.

<< Previous  Top  |  1 | 2 | 3  |  Return to Index  Next >>

  Copyright © 2006-2008  Elizabeth Stapel   |   About   |   Terms of Use

 Feedback   |   Error?