Solving Equations and Proportions

Mrs. Apia's lesson on linear equations in disguise covers rewriting and solving equations that appear non-linear at first glance. The lesson focuses on understanding proportions, using cross products, and applying these concepts to solve equations. Examples include solving complex proportions and using similar triangles to find unknown values. The lesson concludes with a summary of key concepts and methods.

What is the first step in solving a complex proportion?

• Add the numerators

• Divide the numerators by the denominators

• Multiply each numerator by the other fraction's denominator

• Subtract the denominators

How do you solve the equation x/5 = 6/12 using the cross product?

• Divide both sides by 6

• Add 5 to both sides

• Multiply both sides by 12

• Multiply x by 12 and 5 by 6

When dealing with a fraction that has more than one term in the numerator or denominator, what should you remember to do?

• Multiply the terms by zero

• Use the distributive property

• Add the terms together

• Ignore the extra terms

What is the result of simplifying the left side of the equation 3/5 - 63?

• -312/5

• 315/5

• 312/5

• -315/5

What is the correct operation to perform when dividing by a whole number in a fraction?

• Subtract the reciprocal

• Divide by the reciprocal

• Add the reciprocal

• Multiply by the reciprocal

In the context of similar triangles, why is it important to know that the triangles are similar?

• To determine the area of the triangles

• To verify the triangles are congruent

• To confirm that the corresponding sides are in proportion

• To ensure the angles are equal

What is the solution to the equation 12x - 24 = 9.5x + 19?

• x = 17.2

• x = 15.2

• x = 19.2

• x = 12.5

What is the length of side AB if x = 17.2?

• 12.2 cm

• 15.2 cm

• 17.2 cm

• 19.2 cm

What is the length of side AC if x = 17.2?

• 21.2 cm

• 15.2 cm

• 17.2 cm

• 19.2 cm

What is the purpose of using parentheses when dealing with multiple terms in a fraction?

• To add the terms together

• To ensure the distributive property is applied

• To ignore the terms

• To divide the terms by each other