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ALGEBRA READINESS “Solving Addition Equations” (3-1) What is an “equation”? What is an “algebraic equation”? How do you solve an algebraic expression? equation: a mathematical sentence that has an equal sign (both sides are balanced) Example: = 5 algebraic equation: a mathematical sentence that has an equal sign (both sides are balanced) and contains one or more variables. Example: x + 2 = 5 To solve an algebraic expression, you need to isolate the variable (get the variable alone or by itself) on one side of the equal sign. To isolate the variable (letter), you need to work backwards, or “undo” numbers from the variable side by doing their inverse operations (operations which “undo” each other, or cancel each other out). Example: x + 2 = 5 x + 2 = 5 We can use a balanced scale to model this If we took two of the “1” weights from each x = 3 side, we would isolate the “x” weight and both sides would remain balanced, so x = 3.
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ALGEBRA READINESS
LESSON 3-1Warm Up Lesson 3-1 Warm Up
ALGEBRA READINESS
LESSON 3-1Warm Up Lesson 3-1 Warm Up
ALGEBRA READINESS
“Solving Addition Equations” (3-1)
What is an “equation”?
What is an “algebraic equation”?
How do you solve an algebraic expression?
equation: a mathematical sentence that has an equal sign (both sides are balanced)Example: 3 + 2 = 5
algebraic equation: a mathematical sentence that has an equal sign (both sides are balanced) and contains one or more variables.Example: x + 2 = 5
To solve an algebraic expression, you need to isolate the variable (get the variable alone or by itself) on one side of the equal sign. To isolate the variable (letter), you need to work backwards, or “undo” numbers from the variable side by doing their inverse operations (operations which “undo” each other, or cancel each other out).
Example: x + 2 = 5
x + 2 = 5 We can use a balanced scale to model this. - 2 - 2 If we took two of the “1” weights from each x = 3 side, we would isolate the “x” weight and both sides would remain balanced, so x = 3.
ALGEBRA READINESS
“Solving Addition Equations” (3-1)
How do you check to make sure the answer to an algebraic equation is correct?
What is the “subtraction property of equality”?
To check an algebraic equation, substitute (replace) the letter in the original equation with the answer and simplify. If both sides are equal (in other words, the substitution makes the equation a true statement), the answer is correct.
Example: Check x + 2 = 5 for x = 3 3 + 2 = 5 Substitute x for 3 5 = 5 True Statement
Subtraction Property of Equality: If you subtract the same value (number) from both sides of an equation (both sides are equal), the two sides of the equal sign remain equal.
If a = b, then a – c = b – c
Example: If 2 •3 = 6, then 2 •3 – 4 = 6 – 4 2 = 2
ALGEBRA READINESS
Solve h + 9 = 14.
Isolate h on one side of the equation.
Subtract 9 from each side to undo theaddition to isolate h.
h + 9 – 9 = 14 – 9
h + 0 = 5 Inverse Property of Addition
Check h + 9 = 14 Check your solution in the original equation.
h = 5 Identity Property of Addition
14 = 14
(5) + 9 14 Substitute 5 for h.
Solving Addition EquationsLESSON 3-1
Additional Examples
ALGEBRA READINESS
height todayheight last year inches grown
Today Anna discovered that she is 4 in. taller than she was last year at this time. Anna’s height today is 51 in. What was Anna’s height last year at this time?
Let h = Anna’s height last year.
The equation h + 4 = 51 models this situation.
Anna was 47 inches tall.
51h 4
Subtract 4 from each side to undo theaddition.
h + 4 – 4 = 51 – 4
h = 47 Simplify.
Solving Addition EquationsLESSON 3-1
Additional Examples
ALGEBRA READINESS
Solve each equation.
1. 18 + n = 40 2. m + 3.5 = 6.7
3. p + 0.99 = 4.15 4. 78 = q + 20
22 3.2
3.16 58
Solving Addition EquationsLESSON 3-1
Lesson Quiz
