Title: 9. Linear equations
Course: Demonstrating STACK (v4.4.7)

Solve the following equation for [value]: \[ [value] = [value]. \]
\([value]\) =
Feedback: The objective is to get the equation into the form \([value] = p\) where \(p\) is a rational number. To obtain \([value]\) on one side of the equation it may be necessary to under-take several operations which must be performed on both sides of the equation. In this example: \[ [value] = [value]. \] We first move all the constants to one side (\([value]\)): \[ [value] = [value]. \] Then divide by the coefficient of \([value]\) (\([value]\)): \[ [value] = [value]. \] And so we now have obtained a value for [value].

Solve the following equation for [value]: \[ [value] = [value]. \]
\([value]\) =
Feedback: The objective is to get the equation into the form \([value] = p\) where \(p\) is a rational number. To obtain \([value]\) on one side of the equation it may be necessary to under-take several operations which must be performed on both sides of the equation. In this example: \[ [value] = [value]. \] We first move all the constants to one side ([value]): \[ [value] = [value]. \] Then divide by the coefficient of \([value]\) (in this case \([value]\)): \[ [value] = [value]. \] And so we now have obtained a value for [value].

Solve the following equation for [value]: \[ [value] = [value]. \]
\([value]\) =
Feedback: The objective is to get the equation into the form \([value] = p\) where \(p\) is a rational number. To obtain \([value]\) on one side of the equation it may be necessary to under-take several operations which must be performed on both sides of the equation. In this example: \[ [value] = [value]. \] We first collect like terms by moving all the constants to one side and the variables to the other (\([value]\)): \[ [value] = [value]. \] Then divide by the coefficient of \([value]\) (\([value]\)): \[ [value] = [value]. \] And so we now have obtained a value for [value].

Solve the following equation for [value]: \[ [value] = 0.\]
\([value]\) =
Feedback: The objective is to get the equation into the form \([value] = p\) where \(p\) is a rational number. To obtain \([value]\) on one side of the equation it may be necessary to under-take several operations which must be performed on both sides of the equation. In this example: \[ [value] = 0.\] We are first required to expand the brackets and collect like terms: \[ [value] = 0. \] Then move the constants to one side keeping the variables on the other: \[ [value] = [value].\] Then divide by the coefficient of \([value]\) (\([value]\)): \[ [value] = [value]. \] And so we now have obtained a value for [value].

Solve the following equation for [value]: \[ [value] = [value].\]
\([value]\) =
Feedback: The objective is to get the equation into the form \([value] = p\) where \(p\) is a rational number. When fractions are involved it is often best to multiply both sides of the equation by a certain value so that the fractions are removed. In this example: \[ [value] = [value].\] Multiply through by \(10\): \[ [value] = [value]. \] Remove Brackets: \[ [value] = [value]. \] Gather like terms \([value]\): \[ [value] = [value]. \] Finally divide by coefficient of \([value]\) (\(4\)): \[ [value] = [value]. \]