Linear Equations by Example                               -- Part 1.1 -- Solve for x:   x + 12 = 18 Solve Step Check  Subtract 12 from both sides If x = 6, then 6 + 12  = 18      18 = 18   Solve for x:   x + 5 = 20 [Solution]  Solve for x:   3x – 9 = 7 Solve Step Check  Add 9 to both sides Divide by 3   Solve for x:   2x – 8 = 19 [Solution]  Solve for x:  5(x – 2) + 3 = 2(3x – 1) Solve Step Check 5(x – 2) + 3 = 2(3x – 1) Original equation If x = -5, then 5x – 10 + 3 = 6x – 2 Distributive Property      a(b – c) = ab – ac 5(-5 – 2) + 3 = 2(3(-5) – 1) 5x – 7 = 6x – 2        -6x + 7   -6x + 7          -x + 0  =   0  + 5 Combine Like Terms Subtract 6x , Add 7        to both sides 5(-7) + 3 = 2(-15 – 1)                -35 + 3 = 2(-16)                      -32 = -32 -x = 5                  x = -5 Multiply both sides by -1       -x = -1 × x  Solve for x:   6(x – 1) + 4 = 2(4x + 1) [Solution]  Solve for x:  x + 4 = x + 8 Solve Step Check x + 4 = x + 8 Original equation No solution x + 4 = x + 8             -x         -x                            4 = 8 Subtract x from both sides But 4 ¹ 8 There is no number plus 4 can equal the same number plus 8  Solve for x:   2x + 3 = 2x – 4 [Solution] Not all linear equations have solutions.  Can you think of an linear equation that would have more than one solutions.  Solve for x: Solve Step Check  Original equation Multiply both sides by the LCD, 15, to clear fractions. Divide by 11 LCD = 3 × 5 × 1 = 15 4 can be written as 4/1 Rewrite as      [Solution]  Solve for x: Solve Step Factor denominator. Note: x can not be 5 or -5.  You can't have zero in the denominator. Multiply both sides by the LCD to clear fractions. LCD = (x + 5)(x – 5) 4(x – 5) + 2(x + 5) = 32 Check 4x – 20 + 2x + 10 = 32 6x – 10 = 32 6x = 42 x = 7     Solve for x: [Solution]

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joe mcdonald Last Update 09.23.2010