Grade 9 Algebra: Evaluate & Factor Word Problems

A store sells x notebooks for $3 each. Write an expression to represent the total cost of buying 5 notebooks and evaluate it.

• 10

• 20

• 25

• 15

If a rectangle has a length of (2x + 3) meters and a width of (x - 1) meters, write an expression for the area and evaluate it when x = 4.

• 40

• 20

• 28

• 33

A car travels at a speed of (60 - 2x) miles per hour. If x represents the number of passengers, how fast is the car going when there are 5 passengers?

• 40 miles per hour

• 50 miles per hour

• 30 miles per hour

• 60 miles per hour

The sum of two numbers is 12. If one number is represented as (x + 2), write an equation to find the other number and solve for x.

• y = 12 - x

• y = 2x + 10

• y = 10 - x

• y = x + 2

A quadratic expression is given as x^2 - 5x + 6. Factor this polynomial to find its roots.

• (x - 4)(x - 2)

• (x - 2)(x - 3)

• (x - 1)(x - 6)

• (x + 2)(x + 3)

A farmer has a rectangular field with a length of (3x + 2) meters and a width of (x + 1) meters. Write an expression for the perimeter and evaluate it when x = 2.

• 20 meters

• 22 meters

• 24 meters

• 18 meters

The product of two consecutive integers can be expressed as x(x + 1). If the product is 72, write and solve the equation to find the integers.

• 7 and 8

• 6 and 7

• 9 and 10

• 8 and 9

A triangle has a base of (x + 4) cm and a height of (2x - 1) cm. Write an expression for the area and evaluate it when x = 3.

• 15 cm²

• 20 cm²

• 12.5 cm²

• 17.5 cm²

If the expression (x^2 - 9) is factored, what are the values of x that satisfy the equation when set to zero?

• x = -2

• x = 3, x = -3

• x = 2

• x = 0

A rectangular garden has a length of (x + 5) feet and a width of (2x - 3) feet. Write an expression for the area and factor it to find the dimensions when the area is 20 square feet.

• Length = 15/2 feet, Width = 2 feet

• Length = 5 feet, Width = 4 feet

• Length = 10 feet, Width = 3 feet

• Length = 12 feet, Width = 1 foot