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Details for problem "Solve linear equation with distributive element"

Quickname: 3102

Suitable for K-12 grades: Grade 7 Grade 8 Grade 9

Junior High School, Middle School, High School.


Solve a linear equation step-by-step by performing equivalent transformations.


Solve a linear equation step-by-step by performing equivalent transformations. (Example for this math problem)


In a linear equation with one unknown variable, the value of the variable must be determined. The linear equation is formed by a sum of terms of the form ax and/or a on both sides of the equality sign. In addition, there is also a summand in the form of a distributive element a(x+b). By expanding the distributive element, combining like terms and performing equivalence transformation, the equation is to be brought into the form x=c, with c being a whole number. This term represents the solution of the equation. A corresponding note to use the technique of equivalent transformation can be given or omitted in the problem statement.

The number of terms to the left and right of the equality sign that appear together with the distributive element can be predetermined. If desired, only the variable x appears as an unknown in order not to confuse. The individual steps of the solution process can be selected to be

The steps of equivalent transformations are shown in the order:

  1. Multiply out/expand the distributive element
  2. Summarize and rearrange, combine like terms
  3. Move constant to the right side of the equality sign
  4. Move variable elements to the left of the equality sign
  5. Divide by the factor of the variable

The solution is always a whole number.

Topics: Algebra Equations

Tags: Polynom Rules Terms

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Customization options for this problem

Possible values
Number of problems
1, 2, 3, 4, 5, 6
Mention equivalent transformation
Yes, No
Show calculation steps
no, with solution, with problem&solution
Variable always x
Yes, No
Extra terms
1, 2, 3, 4, 5, 6
Distributive element always first
Yes, No

Similar problems

Name and direct link
use Gaussian Algorithm for linear equation system
A system of linear equations is to be solved with the Gaussian elimination method.
Simpler variant, without the distributive element
Solve a linear equation step-by-step by performing equivalent transformations.

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