Question 1

Solve for $$x in $$the equation $$6x + 2 = 7(x - 4). $$What is the value of $$x$$?

Accepted Answer

$$x = 30$$

Question 2

Solve the equation $$4x + 7 - 9x - 8 = 4. $$What is the solution for $$x$$?

Accepted Answer

$$x = -1$$

Question 3

Solve the inequality $$7z \u003e 6z - 15$$ and write the solution in interval notation.

Accepted Answer

$$(-15, \infty)$$

Question 4

Solve the inequality $$5(x + 2) \leq 6(x - 2)$$ and write the solution set in interval notation.

Accepted Answer

$$[22, \infty)$$

Question 5

Find the slope of the line passing through the points $$(2, -6)$$ and $$(8, 1).$$

Accepted Answer

$$\dfrac{7}{6}$$

Question 6

Given $$f(x) = 7x - 13$$ and $$g(x) = \dfrac{1}{7}x + 2$$, are the lines parallel, perpendicular, or neither?

Accepted Answer

Neither

Question 7

Given $$f(x) = -8x - 5$$ and $$g(x) = -8x + 5$$, are the lines parallel, perpendicular, or neither?

Accepted Answer

Parallel

Question 8

Write the equation of the line with slope $$-3$$ passing through $$(-7, 4) in $$the form $$y = mx + b.$$

Accepted Answer

$$y = -3x - 17$$

Question 9

Write the equation of the line with slope $$\dfrac{4}{7}$$ passing through $$(0, 6) in $$the form $$y = mx + b.$$

Accepted Answer

$$y = \dfrac{4}{7}x + 6$$

Question 10

Solve the system of equations:

$$\begin{cases} 2x + y = 4 \ 3x + 2y = 9 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(-1, 6)$$

Question 11

Solve the system of equations:

$$\begin{cases} 5x + 4y = 62 \ 2x + 4y = 68 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(-2, 18)$$

Question 12

Which of the following equations represents a horizontal line?

Accepted Answer

$$f(x) = 3$$

Question 13

A medical researcher is analyzing the relationship between dosage ($$x) $$and patient response ($$y). If $$the data fits the equation $$y = 2x + 5$$, what is the slope and what does it represent?

Accepted Answer

Slope is $$2$$, representing the increase in response per unit increase in dosage.

Question 14

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P = 4x - 20$$, where $$x is $$the number of units sold (in hundreds). What is the break-even point?

Accepted Answer

$$x = 5$$

Question 15

Which of the following graphs passes the vertical line test and is therefore a function?

Accepted Answer

A graph where every vertical line intersects the curve at most once.

Question 16

Graph the inequality $$x - y \u003e -3. $$Which region represents the solution?

Accepted Answer

The region above the line $$x - y = -3 ($$not including the line).

Question 17

A biologist is studying two populations modeled by $$y \geq 2x - 2$$ and $$y \leq -4 - x. $$What region represents the set of possible population pairs?

Accepted Answer

The region where the shaded areas of both inequalities overlap.

Question 18

Which of the following is the correct interval notation for all real numbers greater than $$-15$$?

Accepted Answer

$$(-15, \infty)$$

Question 19

If a line has the equation $$x - 2y = -2$$, what is its slope?

Accepted Answer

$$\dfrac{1}{2}$$

Intermediate Algebra Chapters 2-4 Test: Step-by-Step Study Guidance

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