Solving Equations and Quadratics Flashcard

Front

Avery has 3 times the number of apples as Henry. If Avery gives 5 apples to Henry, she will have 14 apples left. How many apples did Avery originally have?

Back

Answer explanation

To solve for x in the equation 3x + 5 = 14, subtract 5 from both sides to get 3x = 9. Then, divide both sides by 3 to find x = 3. Thus, the correct answer is x = 3.

Tags

CCSS.HSA.REI.A.1

Front

Elijah has $2x - 7$ apples and needs to have 5 apples. What is the first step to find out how many apples he originally had?

Back

Add 7 to both sides

Answer explanation

To isolate the variable x in the equation 2x - 7 = 5, the first step is to eliminate the -7. This is done by adding 7 to both sides, resulting in 2x = 12, which simplifies the equation for further solving.

Tags

CCSS.HSA.REI.A.1

Front

Michael is planning a rectangular garden. The length of the garden is 4 meters more than its width. If the area of the garden is 5 square meters, find the dimensions of the garden.

Back

Width = 1m, Length = 5m

Answer explanation

To solve the equation x^2 - 4x - 5 = 0, we can factor it as (x - 5)(x + 1) = 0. Setting each factor to zero gives x = 5 and x = -1, making the correct answer x = 5, -1.

Tags

CCSS.HSA.REI.B.4

Front

Back

Answer explanation

To solve the equation x^2 + 6x + 9 = 0, we can factor it as (x + 3)(x + 3) = 0. Setting each factor to zero gives x + 3 = 0, leading to x = -3. Thus, the correct answer is x = -3.

Tags

CCSS.HSA.REI.B.4

Front

Back

Answer explanation

To solve the equation x^2 - 2x - 8 = 0, we can factor it as (x - 4)(x + 2) = 0. Setting each factor to zero gives x = 4 and x = -2. Thus, the correct answer is x = 4, -2.

Tags

CCSS.HSA.REI.B.4