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Additional resources for Algebra I (Cliffs Quick Review)
Multiply b = p x q bq = px Then divide both sides by p to get x alone. bq px p = p bq bq p = x or x = p Cross multiplying can be used only when the format is two fractions separated by an equal sign. Be aware that cross multiplying is most effective only when the letter you are solving for is on the bottom (the denominator) of a fraction. If it is on top (the numerator), it is easier simply to clear denominator under the unknown you’re solving for. Example 10: Solve for x. x = p k q 46 CliffsQuickReview Algebra I Multiply both sides by k.
This method involves substituting one equation into another. Example 5: Solve for x and y. x=y+8 x + 3y = 48 From the first equation, substitute (y + 8) for x in the second equation. (y + 8) + 3y = 48 Now solve for y. Simplify by combining y’s. 4y + 8 = 48 -8 -8 4y = 40 4y 40 = 4 4 y = 10 Now insert y = 10 in one of the original equations. x=y+8 x = 10 + 8 x = 18 Answer: y = 10, x = 18 Chapter 5: Equations with Two Variables 53 Graphing method Another method of solving equations is by graphing each equation on a coordinate graph.
Sq rt r = r sq r =t Solving proportions for value Follow the procedures given in Examples 11 and 12 to solve for the unknown. Example 13: Solve for x. 4=2 x 5 Cross multiply. (4)(5) = 2x 20 = 2x Divide both sides by 2. 20 = 2x 2 2 10 = x 48 CliffsQuickReview Algebra I Chapter Checkout Q&A 1. True or false: If a = b and b = c, then a = c. 2. Solve for x: x –5=8 4 3. Solve for x: 7x + 3 = 5x + 7 4. Solve for m: mn – r = q 5. Solve for x: ax = bc 6. Solve for y: m is to n as y is to z. 6 3 7. Solve for x: x = 5 q+r Answers: 1.