Algebra

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These problems are intended to serve as a refresher for basic algebraic skills necessary for the course.

1 :

Simplify the following expression by collecting like terms:

$\sage {a1}\sage {awfa1}+\sage {b1}\sage {awfa1}-\sage {c1}\sage {awfa1}+\sage {d1}\sage {awfa1}-\sage {e1}\sage {awfa1}-\sage {f1}\sage {awfa1}+\sage {g1}\sage {awfa1}+\sage {h1}\sage {awfa1}=\answer {\sage {ans1}}\sage {awfa1}$

2 :

Simplify the following expression by collecting like terms:

$-\sage {a2}\sage {awfa2}+\sage {b2}\sage {awfa2}+\sage {c2}\sage {awfa2}+\sage {d2}\sage {awfa2}+\sage {e2}\sage {awfa2}-\sage {f2}\sage {awfa2}-\sage {g2}\sage {awfa2}+\sage {h2}\sage {awfa2}=\answer {\sage {ans2}}\sage {awfa2}$

3 :

Simplify the following expression by collecting like terms:

$-\sage {a3}\sage {awfa3}-\sage {b3}\sage {awfb3}+\sage {c3}\sage {awfb3}+\sage {d3}\sage {awfa3}+\sage {e3}\sage {awfa3}-\sage {f3}\sage {awfa3}-\sage {g3}\sage {awfb3}+\sage {h3}\sage {awfb3}=\answer {\sage {ans31}}\sage {awfa3}+\answer {\sage {ans32}}\sage {awfb3}$

4 :

Simplify the following expression by collecting like terms:

$\sage {a4}\sage {awfb4}+\sage {b4}\sage {awfa4}+\sage {c4}\sage {awfb4}-\sage {d4}\sage {awfa4}-\sage {e4}\sage {awfb4}-\sage {f4}\sage {awfa4}+\sage {g4}\sage {awfa4}+\sage {h4}\sage {awfb4}=\answer {\sage {ans41}}\sage {awfa4}-\answer {\sage {ans42}}\sage {awfb4}$

5 :

Solve the following expression for $x$ :

$\sage {a5}\sage {coef5}x+\sage {b5}\sage {coef5}=\sage {c5}\sage {coef5}$

$x=\answer {\sage {ans5}}$

6 :

Solve the following expression for $x$ :

$\sage {a6}x+\sage {b6}\sage {coef6}=\sage {c6}\sage {coef6}$

$x=\answer {\sage {ans6}}$

7 :

Solve the following expression for $x$ :

$\sage {a7}\sage {coef7}x+\sage {b7}=\sage {c7}\sage {coef7}$

$x=\answer {\sage {ans7}}$

8 :

Solve the following expression for $x$ :

$\sage {a8}\sage {coef8}x+\sage {b8}\sage {coef8}=\sage {c8}$

$x=\answer {\sage {ans8}}$