Solving Basic and Advanced Equations with Addition and Subtraction
In this guide, we will explore various mathematical expressions and their solutions, using specific values for x, y, and z. Learn to solve both basic and advanced equations, like x + 2 = 6, with clear steps and examples. We will cover the Subtraction and Addition Properties of Equality, enabling you to manipulate equations confidently. Real-world examples, such as calculating the lengths of fish and costs of items, will be provided to help solidify your understanding.
Solving Basic and Advanced Equations with Addition and Subtraction
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Presentation Transcript
POD Solve each expression if x=4, y=7, and z=5 basic advanced 3x + y2 − (-z) x + y +12 3(4) + 72 − (-5) 4 + 7 +12 3(4) + 49 − (-5) 11 +12 12 + 49 − (-5) 23 61 − (-5) 61 + 5 66
One-Step Addition and Subtraction Equations An equation is a sentence stating that two quantities are equal. x + 2 = 6 x = 4 These are equivalent equations because they have the same solution, 4 The value of a variable that makes an equation true is called the solution of the equation.
Remember these steps: Get the variable alone To do that, do the opposite of what you are already doing to it. Whatever you do to one side, you must do to the other.
The Subtraction Property of Equality states that the two sides of an equation remain equal when you subtract the same number from each side. If a=b, then a−c = b−c Example: check x + 6 = 4 -2 + 6 = 4 −6 −6 4 = 4 x = -2
The Addition Property of Equality states that the two sides of an equation remain equal when you add the same number from each side. If a=b, then a+c = b+c Example: check X − 2 = 1 3− 2 = 1 +2 +2 1 = 1 x = 3
Whiteboard time: y + 6 = 9 -6 -6 y = 3
Whiteboard time: x + 3 = 1 -3 -3 x = -2
Whiteboard time: -3 = a + 4 -4 -4 -7 = a
Whiteboard time: y − 3 = 4 +3 +3 y = 7
Whiteboard time: r − 4 = -2 +4 +4 r = 2
Whiteboard time: An angelfish can grow to be 12 inches long. If an angelfish is 8.5 inches longer than a clownfish, how long is a clownfish? 12 = c + 8.5 -8.5 - 8.5 3.5 = c A clownfish is 3.5 inches long
Whiteboard time: A pair of shoes costs $25. This is $14 less than the cost of a pair of jeans. Find the cost of the jeans? 25 = j − 14 +14 +14 39 = j The jeans cost $39.
