2 1 The Addition Property of Equality Linear

Linear Equation in One Variable • An eqn. that can be written in the

Solutions to Equations - number(s) that when substituted in place of the variable satisfy

Addition Property of Equality • Adding (or subtracting) the same nonzero number to (from)

Equivalent Equations -2 or more eqns. with the same soln. set

When solving an eqn. , need x by itself on one side of the

5=b+5 5– 5=b+5– 5 0=b b=0 {0} Check: 5=b+5 5=0+5 5=5

Solving an eqn. using the Add. Prop. Of Equality • Use dist. prop. To

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2. 1 The Addition Property of Equality

Linear Equation in One Variable • An eqn. that can be written in the form ax + b = c, where a ≠ 0 Ex: LE in 1 var: 2 x + 1 = 5 4 x = 7 X = -3 Not LE in 1 var: x 2 + 8 x = -11

Solutions to Equations - number(s) that when substituted in place of the variable satisfy the equation (make a true statement). Ex: Is 2 a soln. of 3 x 2 – 7 = 12? 3(2)2 – 7 = 12 3(4) – 7 = 12 12 – 7 = 12 5 = 12 False, so 2 is NOT a soln.

Addition Property of Equality • Adding (or subtracting) the same nonzero number to (from) both sides of an eqn, will not change the soln. If then a=b a+c=b+c keep equation “balanced”

Equivalent Equations -2 or more eqns. with the same soln. set

When solving an eqn. , need x by itself on one side of the eqn. Ex: Solve. Check: x– 3=7 x– 3+3=7+3 x = 10 {10} x– 3=7 10 – 3 = 7 substitute 10 for x 7 = 7 true so 10 is a soln.

5=b+5 5– 5=b+5– 5 0=b b=0 {0} Check: 5=b+5 5=0+5 5=5

4 x – 3 – 8 x + 1 = -5 x + 9 -4 x – 2 + 5 x = -5 x + 9 + 5 x x– 2=9 x– 2+2=9+2 x = 11 {11}

Solving an eqn. using the Add. Prop. Of Equality • Use dist. prop. To get rid of parentheses • Combine like terms on each side separately • Add/Sub. terms to get all variable terms on one side of the eqn. and all constants on the other side