Question 1

Solve the equation $$5x - 7 = 2x + 8$$ for $$x.$$

Accepted Answer

$$x = 5$$

Question 2

Express the solution set of $$-3 \u003c 4x + 1 \leq 9 in $$interval notation.

Accepted Answer

$$(-1, 2]$$

Question 3

Solve for $$x in $$the equation $$2(x - 5) = 3x + 2.$$

Accepted Answer

$$x = -2$$

Question 4

Determine the domain and range for the relation $$\{(3,3), (1,-1), (8,-3), (1,6)\}.$$

Accepted Answer

Domain: $$\{1, 3, 8\}$$, Range: $$\{-1, 3, -3, 6\}$$

Question 5

Given $$y = -2x + 4$$, identify the slope and $$y-$$intercept, then sketch the graph.

Accepted Answer

Slope: $$-2$$, $$y-$$intercept: $$4$$

Question 6

A savings account is started at $$1000$$ dollars with an interest rate of $$5\%$$ per year, compounded annually. What will the balance be after $$3$$ years? (Round to the nearest dollar)

Accepted Answer

$$1158$$

Question 7

A customer pays $$34.40$$ for $$5$$ items, some at $$5.00$$ each and some at $$8.00$$ each. How many of each item did the customer buy?

Accepted Answer

$$2 at$$ $$5.00$$, $$3 at$$ $$8.00$$

Question 8

Solve the system of equations: $$2x + 3y = 10$$ and $$x - y = 1.$$

Accepted Answer

$$x = 3, y = 2$$

Question 9

If the length of a rectangle is $$3$$ units less than twice the width, and the perimeter is $$18$$ units, what are the dimensions of the rectangle?

Accepted Answer

Width: $$3$$ units, Length: $$6$$ units

Question 10

Solve the quadratic equation $$x^2 - 4x + 1 = 0$.

Accepted Answer

$$x = 2 \pm \sqrt{3}$$

Question 11

Which of the following is the solution to the inequality $$2x - 5 \u003e 3x + 2$$?

Accepted Answer

$$x \u003c -7$$

Question 12

Given the function $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 13

Solve for $$x$$: $$2x - 5 = 3x + 2.$$

Accepted Answer

$$x = -7$$

Question 14

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 15

Solve the equation $$2x - 5 = 3x + 2$$ for $$x.$$

Accepted Answer

$$x = -7$$

Question 16

Which of the following intervals represents the solution to $$-3 \u003c 4x + 1 \leq 9$$?

Accepted Answer

$$(-1, 2]$$

Question 17

If $$f(x) = 2x - 5$$, what is $$f^{-1}(x$$)$$, the inverse function?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+5}{2}$$

Question 18

Solve for $$x in $$the equation $$2x - 5 = 3x + 2$$ and interpret the solution in the context of a real-world scenario where $$x$$ represents the number of years until two investments are equal in value.

Accepted Answer

$$x = -7$$, so the investments will never be equal in the future.

Key Concepts and Problem Types in College Algebra: Equations, Inequalities, Functions, and Applications

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