Solving Linear Equations

To solve a linear equation, clear any parentheses and isolate the variable. Recall that a linear equation only involves the independent variable (x) to the first power (that, is, it has no terms like x2, 1/x, sin(x), etc.).

Examples
Before looking at how these are solved, be sure it is clear why they are linear. Then check that you see the algebraic steps in clearing the parentheses and isolating the variable.
  1. Solve for x:
    3 - (5.4 + 2(4.3 - x)) = 2 - (0.3x - 0.8)
    3-(5.4+8.6-2x)=2-0.3x+0.8, so 3-14+2x=2.8-0.3x, or 2.3x=13.8, so x=6.
  2. Solve for q:
    p^2q + r(-q-1) = 4(p+r)
    p^2q-rq-r=4p+4r, so q(p^2-r) = 4p+5r, and q=(4p+5r)/(p^2-r)
Practice

Be sure you've gone through each step in the examples above before doing these. Once you've worked them until you're sure that you understand them, go on to the next section. There are more problems of this type in the section test at the end of the section.

Note that you can get new practice problems by clicking the "Refresh" button at the bottom of the practice set.

  1. Solve for x:
    a   -   b ( c x   +   d ( x   -   g ) )   =   h x   -   ( x   +   j )   +   k
    Answer:   x =
    (Enter answers, then click: . Answer message: )
  2. Then, again solve for x:
    m ( x   +   n ( x   +   p ( x   +   q ) ) )   =   r ( x   -   s ( x   -   t ( x   -   u ) ) )
    Answer:   x =
    (Enter answers, then click: . Answer message: )
For more practice, click: .
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precal: 7.2 - solving linear eq
page created: Tue Nov 26 20:47:25 2024
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