Lesson 1-0 Algebra Review

Language of Math Language of Math is EQUATIONS! All work should be done with equations All calculations should have equations 3x + 20 – 4x – 10 is an expression; not an equation!

Rules of Equality Add the same value to both sides of the equation Subtract the same value to both sides of the equation Multiply both sides of the equation by the same value Divide both sides of the equation by the same value

Typical Geometry Problems Solve for x in the following: 6x – 12 = 4x + 18 (6x – 12) + (4x + 22) = 180 5x + (2x – 10) + (3x + 30) + 2x + (4x + 40) = 540

Problem 1 Solve for x in the following: 6x – 12 = 4x + 18 + 12 = + 12 + 12 = + 12 6x = 4x + 30 - 4x = - 4x 2x = 30 x = 15

Problem 2 Solve for x in the following: (6x – 12) + (4x + 22) = 180

Problem 3 Solve for x in the following: 5x + (2x – 10) + (3x + 30) + 2x + (4x + 40) = 540 16x + 60 = 540 16x = 480 x = 30

Common Mistakes Add or subtracting the same value to both sides of a plus or minus; instead of both sides of the equation! Combining constants and coefficients of variables Adding instead of multiplying Subtracting instead of dividing

Check your Answer! Homer Simpson test: Does the answer make any sense? Common warning signs: Never have a negative measure for angles or distance Almost never will x = negative number in Geometry (except on graphing problems)

Magic Geometry Numbers 90 – complementary (seen in right triangles!) 180 – supplementary (also seen in all triangles) 360 – once around a circle in angles or arcs

Round Two Solve for x in the following: 8x – 12 = 4x + 28 (6x – 12) + (9x + 27) = 180 x + (2x + 20) + (4x – 10) + 2x + (4x – 40) + 2x = 720

Round Two – Problem 1 Solve for x in the following: 8x – 12 = 4x + 28 + 12 = + 12 8x = 4x + 40 - 4x = - 4x 4x = 40 x = 10

Round Two – Problem 2 Solve for x in the following: (6x – 12) + (9x + 27) = 180 15x + 15 = 180 15x = 165 x = 11

Round Two – Problem 3 Solve for x in the following: x + (2x + 20) + (4x – 10) + 2x + (4x – 40) + 2x = 720 15x – 30 = 720 15x = 750 x = 50