Question

How do you solve for x in \[ax + b = cx + d\] \[?\]

Answer 1

Hint: Here in this given equation is a system of linear equations. Here we have to solve for x variable. To solve x for using a multi-step equation. we can shift the x variable to LHS by subtract cx and b from both sides then isolate \[x\] using distributive property, and for further simplification divide both sides by \[\left( {a - c} \right)\] .

Complete step-by-step answer:
A system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables.
To solve x in a given system of linear equations by using multi-step equations. Multi-step equations are algebraic expressions that require more than one operation, such as subtraction, addition, multiplication, division, or exponentiation, to solve.
Consider the given system of linear equation
 \[ \Rightarrow \,\,\,ax + b = cx + d\]
Now we have to solve this equation for x in terms of a, b, c, and d.
Let subtract cx from both sides, then
 \[ \Rightarrow \,\,\,ax + b - cx = cx + d - cx\]
 \[ \Rightarrow \,\,\,ax + b - cx = d\]
And further subtract b from both sides, then
 \[ \Rightarrow \,\,\,ax + b - cx - b = d - b\]
 \[ \Rightarrow \,\,\,ax - cx = d - b\]
Take x common on LHS or isolate x by using distributive property
 \[ \Rightarrow \,\,\,x\left( {a - c} \right) = d - b\]
To solve x, divide both sides by \[\left( {a - c} \right)\] .
 \[ \Rightarrow \,\,\,\dfrac{{x\left( {a - c} \right)}}{{a - c}} = \dfrac{{d - b}}{{a - c}}\]
 \[\therefore \,\,\,\,\,\,x = \dfrac{{d - b}}{{a - c}}\]
Hence we have solved the given equation.
Hence, the value of x in the system of linear equations \[ax + b = cx + d\] is \[x = \dfrac{{d - b}}{{a - c}}\] .
So, the correct answer is “ \[x = \dfrac{{d - b}}{{a - c}}\] ”.

Note: The equation is an algebraic equation, where it is a combination of variables and the constants. Group the variable in one side of the equation and the constant terms to the other side of the equation. By using the arithmetic operations, we are simplifying the given question. The question is about the general form.