Page 118 - Algebra 1

L E S S O N Solving One-Step Equations by Adding or
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Subtracting
Warm Up
New Concepts
1. Vocabulary -4 and 4 are because they have the same absolute
(6)
value but different signs. 2. Add 7.5 + (-1.25).
(5)
3. Subtract 12.75 - (-1.05). (6)
4. Use <, >, or = to compare 6x + 3 and -2x + 4 when x = -3. (16)
5. Evaluate w - (wy - y) for w = -4 and y = -1.
(9)
A 1 B -1 C -9 D 9
An equation is a statement that uses an equal sign to show that two quantities are equal. A solution of an equation in one variable is a value of the variable that makes the equation true.
Identifying Solutions
State whether the value of the variable is a solution of the equation.
a. x + 6 = 9 for x = 3 b. x - 6 = 9 for x = 3 SOLUTION SOLUTION
x+6=9 x-6=9
Example
1
Math Reasoning
Verify If the same quantity is added to both sides of x - 7 = 15, show that the resulting equation is equivalent to x - 7 = 15.
(3) + 6 9 Substitute 3 for x. 9=9 ✓
Solution, 3 + 6 = 9
An equation is like a balance scale.
(3) - 6 9 Substitute 3 for x. -3≠9 ✗
Not a solution, 3 - 6 ≠ 9
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Online Connection www.SaxonMathResources.com
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equivalent equations
x+6=9 x=3
The scale remains balanced when the same quantity is added to both sides, or
when the same quantity is subtracted from both sides.
Equivalent equations have the same solution set. By adding or subtracting the same quantity from both sides of an equation, each equation remains equivalent to the original equation. Furthermore, each side of the equation remains balanced as the equation is solved.
Lesson 19 103