3 1 Solving Equations Using Addition and Subtraction

3. 1 Solving Equations Using Addition and Subtraction 10 -24 -13

Vocabulary • Equivalent equations • x + 3 = 5 and x = 2 • Inverse Operations • two operations that undo each other • Linear Equation • an equation in which the variable of the exponent is one (x + 5 = 9)

Transforming Equations • To transform an equation you can add or subtract the same number to both sides or simplify one or both sides. • Examples: • x-3=5 • x + 6 = 10 • x=8 -3 Add 3 x=8 Subtract 6 x=4 Simplify x=5

Simplify first • -8 = n - (-4) • -8 = n + 4 • -8 - 4 = n • -12 = n • Check your solution • -8 = -12 - (-4) -8 = -8 ✓

Problem Solving • • • You can write linear equations to model many real life situations. On January 22 nd, 1943, the temperature in Spearfish fell from 54 degrees F at 9: 00 am to -4 degrees F at 9: 27 am. Write and solve a linear equation to find how many degrees the temperature fell. 1. ) Verbal model • Temp at 9: 27 = Temp at 9 am - degrees fallen

• Label your verbal model to write an algebraic model, let T = degrees fallen • -4 = 54 - T • Subtract 54 from both sides • -58 = -T • 58 = T, the temperature fell by 58 degrees

Practice Problems - do these in your notebook • Solve the Equation. • 1. ) r + 3 = 2 • 2. ) -1 = t - 6 • 3. ) x + 4 - 3 = 9 • 4. ) r - (-2) = 5

Problem Solving Practice • You put some money in your pocket. You spend $4. 50 on lunch. You have $7. 50 in your pocket after buying lunch. Write an equation to find how much money you had before lunch. • M - 4. 50 = 7. 50 • M = $12. 00

3. 1 Homework • P. 135 -136 #26 -56 even