Question 1

Translate the following sentence into an algebraic equation: "x is 25% of 200." Which equation correctly represents the sentence?

Accepted Answer

$$x = 0.25 	imes 200$$

Question 2

Why does the equation $$|x| = -3$$ have no real solutions?

Accepted Answer

Because absolute value represents distance, which cannot be negative, no real $$x$$ has distance $$-3$$ from zero.

Question 3

Solve the inequality $$x - 7 \u003e 2.$$

Accepted Answer

$$x \u003e 9$$

Question 4

If $$-2x \u003c 6$$, what is the correct solution for $$x$$ after isolating the variable?

Accepted Answer

$$x \u003e -3$$

Question 5

Which algebraic translation correctly represents: "There are eight more nickels than dimes," if $$d$$ represents the number of dimes and $$n$$ represents the number of nickels?

Accepted Answer

$$n = d + 8$$

Question 6

Solve: $$4(x - 2) = 3x + 5. $$Which value of $$x$$ satisfies the equation?

Accepted Answer

$$x = 13$$

Question 7

Which symbol denotes the intersection of sets $$A$$ and $$B$$?

Accepted Answer

$$A \cap B$$

Question 8

Which phrase from the following sentence signals that you should introduce a variable to represent an unknown quantity? Sentence: "The number of apples a student picks."

Accepted Answer

"The number" or "the number of apples"

Question 9

Simplify and solve: $$-3(2x + 5) + 4x = 7.$$

Accepted Answer

$$x = -11$$

Question 10

The formula for the volume of a triangular prism is $$V = \frac{1}{2}bhL$$, where $$b$$ and $$h$$ are the base and height of the triangular face, and $$L is $$the length of the prism. If $$b = 6 cm$$, $$h = 8 cm$$, and $$L = 10 cm$$, compute $$V by $$substituting these values into the formula.

Accepted Answer

$$240\ 	ext{cm}^3$$

Question 11

Given the standard-form inequality $$5x - 10y \leq 20$$, write the boundary line in slope-intercept form.

Accepted Answer

$$y = -\frac{1}{2}x + 2$$

Question 12

Which mapping diagram corresponds to the ordered pairs $$(1, 2)$$, $$(3, 4)$$, and $$(1, 5)$$?

Accepted Answer

A diagram where $$1$$ points to $$2$$ and $$5$$, and $$3$$ points to $$4$$

Question 13

A line passes through the points $$(3, 5)$$ and $$(0, -2). $$From these points, what is the $$y-$$intercept of the line?

Accepted Answer

$$-2$$

Question 14

What does the notation $$f(x)$$ represent in the context of functions relating $$x$$ and $$y$$?

Accepted Answer

The output $$y$$ corresponding to the input $$x$$

Question 15

For the equation $$4x + 2y = 8$$, if you choose $$x = 1$$, what is the corresponding $$y$$ and which point do you plot?

Accepted Answer

$$(1, 2)$$

Question 16

Which of the following is the best definition of an ordered-pair solution to a two-variable linear equation?

Accepted Answer

An ordered pair $$(x, y)$$ that, when substituted into the equation, makes both sides equal; it corresponds to the single point with coordinates $$x$$ and $$y on $$the coordinate plane.

Question 17

Find the slope of the line through the points $$(4, -2)$$ and $$(1, 4)$$ using the slope formula.

Accepted Answer

$$-2$$

Question 18

Which statement correctly describes the roles of the $$x-$$axis and $$y-$$axis in the Cartesian plane?

Accepted Answer

The $$x-$$axis is horizontal and represents left–right movement, while the $$y-$$axis is vertical and represents up-down movement. Together, they form the rectangular coordinate system.

Question 19

Write the equation of the line in point-slope form that has slope $$m = 3$$ and passes through the point $$(4, -1).$$

Accepted Answer

$$y + 1 = 3(x - 4)$$

Intermediate Algebra Exam 1 Study Guidance (Ch 2 & 3)

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