Algebra

You will be able to

• Determine the solutions of |ax + b| = |cx + d| by squaring both sides, and of |ax + b| = c or |ax + b| = cx + d by taking both cases.
• Determine the solution set of an inequality such as |x − a| < b or 2x + 5 < |x + 1|, and show it on a number line and as the part of the V below or above the other graph.
• Explain why a root that makes the other side negative is rejected, and check every solution in the original equation.

You will be able to

• State the form of the partial fractions for a denominator of distinct linear factors, a repeated linear factor (a term for every power), or a linear factor and a quadratic cx² + d.
• Determine the constants by substituting the root of each linear factor and by comparing coefficients, and write the fraction in partial fractions.
• Explain why a wrong form, such as one that leaves out C/(cx + d)², cannot equal the fraction, by comparing coefficients and testing at a value of x.