Question 1

Solve for $$x$$: $$9x - 5 = 7 + 4x.$$

Accepted Answer

$$x = \dfrac{12}{5}$$

Question 2

Which of the following is the solution to $$3(7x - 5) - (6x - 9) = 5x + 12$$?

Accepted Answer

$$x = \dfrac{19}{10}$$

Question 3

Simplify the expression $$(6 + 5i) - (8 - 6i)$$, where $$i is $$the imaginary unit.

Accepted Answer

$$-2 + 11i$$

Question 4

Solve for $$x$$ using the square root property: $$6x^2 = 150$.

Accepted Answer

Question 5

Solve the quadratic equation $$x^2 + 7x + 4 = 0$ by completing the square.

Accepted Answer

$$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$$

Question 6

Which of the following is the solution to $$x^2 + 2x + 26 = 0$ using the quadratic formula?

Accepted Answer

$$x = -1 \pm 5i$$

Question 7

Solve the inequality $$6x - 5 \leq 8$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, \dfrac{13}{6}]$$

Question 8

Given the equation $$\sqrt{8} (\sqrt{3} - \sqrt{7})$$, simplify the expression.

Accepted Answer

$$2\sqrt{6} - 2\sqrt{14}$$

Question 9

Solve for $$x$$: $$(x - 2)^2$ = 96.$$

Accepted Answer

$$x = 2 \pm 4\sqrt{6}$$

Question 10

Solve the equation $$4x - 3x^2$ = 0.$$

Accepted Answer

$$x = 0 or$$ $$x = 1$$

Question 11

Which of the following is the solution to $$6x^2 = 150$?

Accepted Answer

Question 12

Solve the inequality $$-55 \u003c 3x + 13 \leq 34$$ and express the solution in interval notation.

Accepted Answer

$$(-6, 7]$$

Question 13

Simplify $$(-4 + 8i) + (4 + 8i).$$

Accepted Answer

$$0 + 16i$$

Question 14

Solve for $$x$$: $$x^2 + 7x + 4 = 0$ using the quadratic formula.

Accepted Answer

$$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$$

Question 15

Given $$x^2 + 2x + 26 = 0$, what are the solutions?

Accepted Answer

$$x = -1 \pm 5i$$

Question 16

Solve the inequality $$72 + 4x \u003c 18$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -14)$$

Question 17

If $$x^2 + 2x + 26 = 0$ models the height of a projectile in meters, what does the solution x = -1$$ \pm 5i$$ indicate about the projectile?

Accepted Answer

The projectile never reaches the ground (no real solution).

Question 18

Solve for $$x$$: $$6x - 5 \leq 8.$$

Accepted Answer

$$x \leq \dfrac{13}{6}$$

Question 19

Which of the following is the solution to $$x^2 + 2x + 26 = 0$ using the quadratic formula?

Accepted Answer

$$x = -1 \pm 5i$$

College Algebra: Solving Equations, Simplifying Expressions, and Solving Inequalities

스터디 가이드 - 연습 문제