Iowa Algebra

Consider the inequality below. 3x + 2 < 20 To solve the inequality for x in the fewest number of steps, what is the most logical first step?

• Subtract 2 from both sides of the inequality.

• Multiply both sides of the inequality by 3.

• Divide both sides of the inequality by 3.

• Add 2 to both sides of the inequality.

• Reverse the < sign to a > sign.

Answer explanation

The most logical first step is to subtract 2 from both sides of the inequality to isolate the variable x.

What is the y-intercept of the graph of the equation 3x - 6y = 12?

• (0, -4)

• (0, -2)

• (0, 2)

• (0, 4)

• (0, -6)

Answer explanation

The y-intercept is found by setting x=0 in the equation, giving -6y=12, which simplifies to y=-2. Therefore, the y-intercept is (0, -2).

If 5x - 2 = 3x + 6, what is the value of x?

• 2

• 4

• 6

• 8

Imagine two gardens, Garden C and Garden D. Garden C is perfectly square, while Garden D is rectangular. Garden D's length is 3 feet longer than one side of Garden C, and its width is 1 foot shorter than the same side of Garden C. If both gardens have the same area, which equation could be used to find the length in feet, y, of one side of Garden C?

• (y+3) * (y-1)=y * y

• (y-3) * (y+1)=y * y

• (y+3) * (y-1)=2 * y * y

• (y-3) * (y+1)=2 * y * y

Answer explanation

Choose the equation where the area of Garden C is equal to the product of (y+3) and (y-1), which is (y+3) * (y-1)=y * y

What is the value of y in the solution to this system of equations? 3x - 5y = 22 y = -5x + 32

Mathematical Equivalence

ON

Graph the solution to the system. The first equation has been plotted for you.

y = -3x-3

y= 4x +4

What is the slope of the line that passes through the points (10, -5) and (0, 15)?

• -2

• 2

• -1/2

• 1/2

• 0

Answer explanation

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). Substituting the values, we get (-5 - 15) / (10 - 0) = -20 / 10 = -2. Therefore, the slope is -2.

A bike shop calculates the resale value of a used bicycle based on the information in the following table. What equation best describes the relationship between the resale value in dollars, v, of the bicycle and the number of years, x, since the bicycle was bought?

• v=800-50x

• v=800-100x

• v=850-50x

• v=850-100x

• v=900-100x

Answer explanation

The correct equation is v=850-100x because the resale value starts at $850 and decreases by $100 for each year since the bicycle was bought.

Which number line represents the solution set for the inequality below when x is a real number? 3x + 4 > 2x - 5

• The number line with an open circle at -9 and an arrow to the right.

• The number line with an open circle at 2 and an arrow to the left.

• The number line with a closed circle at -9 and an arrow to the right.

• The number line with an open circle at -3 and an arrow to the left.

Answer explanation

The correct answer is the number line with an open circle at -9 and an arrow to the right, indicating the solution set for the given inequality.

Simplify the expression below.

(9 + 4y) - (3 - 2y)

• 6 + 6y

• 9 + 4y - 3 + 2y

• 12 + 6y

• 6 + 2y

Answer explanation

To simplify the expression, distribute the negative sign in the second parenthesis. Then combine like terms to get 6 + 6y.