Rearranging Equations and Formulas with Inverse Operations

The video tutorial on 'The Magic of Math' channel covers rewriting equations and formulas. It begins with an introduction to literal equations, explaining their use with multiple variables. The lesson progresses to demonstrate how to rewrite equations in different forms, such as slope-intercept and standard form, using inverse operations. The tutorial also covers rewriting formulas to solve for specific variables, using examples like the area of a triangle and the volume of a pyramid. Finally, it addresses solving complex equations with multiple variables, emphasizing factoring techniques.

What is a literal equation?

• An equation with only one variable

• An equation with no variables

• An equation written using two or more variables

• An equation that cannot be solved

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CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.4

Which form of an equation is most commonly used to find the x and y-intercepts?

• Quadratic form

• Slope-intercept form

• Point-slope form

• Standard form

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CCSS.HSA.REI.D.11

What is the first step in solving the equation 4x + 2y = 12 for y?

• Subtract 4x from both sides

• Add 4x to both sides

• Divide both sides by 2

• Multiply both sides by 2

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CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.1

When converting from point-slope form to slope-intercept form, what should you do first?

• Add the y-intercept

• Distribute the slope

• Combine like terms

• Subtract the x-term

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CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

How do you clear the fraction in the formula for the area of a triangle when solving for height?

• Divide both sides by 2

• Multiply both sides by 1/2

• Subtract the base from both sides

• Multiply both sides by 2

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CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.1

What is the formula for the height of a triangle if you know the area and the base?

• h = A / 2b

• h = b / 2A

• h = 2A / b

• h = A / b

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CCSS.HSA.CED.A.4

In the formula for the volume of a pyramid, what is the reciprocal of 1/3?

• 3

• 1/3

• 1/2

• 2

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CCSS.5.NF.B.3

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What is the first step in solving a more complex equation with two terms containing the variable x?

• Combine like terms

• Factor out the x

• Add the terms together

• Divide both sides by x

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CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

How do you isolate x in the equation y = x(6 - h)?

• Add 6 to both sides

• Multiply both sides by (6 - h)

• Divide both sides by (6 - h)

• Subtract h from both sides

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CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

What is the final step in solving the equation y = x(k - 7) for x?

• Divide both sides by (k - 7)

• Subtract 7 from both sides

• Add k to both sides

• Multiply both sides by (k - 7)

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CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3