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generate core steps for solving an equation for a given variable


Calling Sequence



Package Usage



Calling Sequence

Student[Basics][LinearSolveSteps]( expr, var )

Student[Basics][LinearSolveSteps]( expr, var, implicitmultiply = true )




equation or string containing an equation



symbol (variable to solve for)



(optional) true or false



The LinearSolveSteps command accepts a linear equation expr in the given variable, var, and displays the steps required to solve for that variable.


Note that this command also accepts some nonlinear equations that can be reduced down to linear equations (in other words, you can isolate x on one side of the equation, and there is only one solution).


If expr is a string, then it is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.  


The implicitmultiply option is only relevant when expr is a string.  This option is passed directly on to the InertForm:-Parse command and will cause things like "2x" to be interpreted as 2*x, but also, "xyz" to be interpreted as x*y*z.


A step may show up where the expression is not obviously different from the previous step.  This can happen when the underlying data structure is transformed during the step, and it is not obvious that the resulting structure is the same as the original, but just expressed differently.  This becomes more apparent when looking at the inert-form of the raw data.


The return value is a module that display annotated steps by default.  This module also has callable methods and data members: data, numsteps, step, and toMathML.  

data: a numsteps x 2 array where column 1 is the inert-form expression, and column 2 is the annotation.  R:-data[1,1] is the original expression in inert-form.

numsteps: the number of steps in the solution, including the original expression.  

step(i): a method for displaying individual steps.  Calling R:-step(i) will display the ith typeset expression and annotation.  Step 1 is the original expression.

toMathML(): a method for converting the sequence of steps and annotations into mathml.  The toMathML command optionally takes one or two arguments: (1) a filename, indicating the mathml should be written to the specified file, and (2) the option htmlheader=true, which will also cause html tags to be written along with the mathml, thus generating a complete .html page that can be loaded in a browser.

Package Usage


This function is part of the Student[Basics] package, so it can be used in the short form LinearSolveSteps(..) only after executing the command with(Student[Basics]). However, it can always be accessed through the long form of the command by using Student[Basics][LinearSolveSteps](..).



LinearSolveSteps( (x+1)/(2*y*z) = 4*y^2/z + 3*x/y, x );

?=??=?subtract from both sides?=?find common denominator?=?sum over common denominator?=?distributive multiply?=?multiply constants?=?reorder terms?=?factor?=?divide6xz+x+1=?multiply rhs by denominator of lhs?=?subtract from both sides?=?multiply fraction?=?divide?=?factorx=?divide both sides


Note that the result is a module with callable methods

ex := LinearSolveSteps( 1/x - 1/2 = 3/4 - 2/x, x );

ex?=??=?subtract from both sides?=?distribute negation3x=?add terms3x=?distribute negation3x=54add termsx3=45reciprocal of both sidesx=?multiply rhs by denominator of lhsx=?multiply fraction






?=?subtract from both sides



<math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>-1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mo>=</mo><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>-2</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mrow></mrow></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>-2</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mrow><mo>=</mo><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>-1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mrow><mspace width='10px'><mtext color='blue'>( subtract from both sides )</mtext></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mrow><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mfrac><mn>2</mn><mi>x</mi></mfrac></mrow><mo>=</mo><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>-1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mrow><mspace width='10px'><mtext color='blue'>( distribute negation )</mtext></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mfrac><mn>3</mn><mi>x</mi></mfrac><mo>=</mo><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>-1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mrow><mspace width='10px'><mtext color='blue'>( add terms )</mtext></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mfrac><mn>3</mn><mi>x</mi></mfrac><mo>=</mo><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mrow><mspace width='10px'><mtext color='blue'>( distribute negation )</mtext></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mfrac><mn>3</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>4</mn></mfrac></mrow><mspace width='10px'><mtext color='blue'>( add terms )</mtext></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mfrac><mi>x</mi><mn>3</mn></mfrac><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></mrow><mspace width='10px'><mtext color='blue'>( reciprocal of both sides )</mtext></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mi>x</mi><mo>=</mo><mrow><mn>3</mn><mo> </mo><mfenced><mfrac><mn>4</mn><mn>5</mn></mfrac></mfenced></mrow></mrow><mspace width='10px'><mtext color='blue'>( multiply rhs by denominator of lhs )</mtext></mstyle></math> <math xmlns=''><mstyle scriptminsize='8.0pt'><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow><mspace width='10px'><mtext color='blue'>( multiply fraction )</mtext></mstyle></math>


The input can be a string, which prevents automatic simplification

LinearSolveSteps( "x + 3^2 = 12", x );

?=12x=?subtract from both sidesx=?evaluate powerx=3add terms


The implicitmultiply option allows short-hand for string input.

LinearSolveSteps( "3(x-2) = 0", x, 'implicitmultiply' );

?=0?=0distributive multiply?=0multiply constants3x=6subtract from both sidesx=?divide both sidesx=2reduce fraction by gcd




The Student[Basics][LinearSolveSteps] command was introduced in Maple 18.


For more information on Maple 18 changes, see Updates in Maple 18.

See Also