Question 1

Solve for $$x$$: $$\frac{3x^2$}{2} = 28x - 3$$

Accepted Answer

$$x = 7,\ x = -\frac{1}{3}$$

Question 2

Solve for $$x$$: $$\frac{2x - 3x}{12} = 1 - 4$$

Accepted Answer

$$x = -60$$

Question 3

Solve for $$x$$: $$\frac{3x + 9}{5} = 12$$

Accepted Answer

$$x = 11$$

Question 4

Solve for $$x$$: $$\frac{2x - 1}{x + 3} = -9$$

Accepted Answer

$$x = -\frac{28}{11}$$

Question 5

Solve for $$x$$: $$\frac{x + 1}{x + 4} = 3$$

Accepted Answer

$$x = \frac{5}{2}$$

Question 6

A chemist mixes a solution with a concentration of $$x$$ grams per liter. If $$\frac{3x + 9}{5} = 12$$, what is the concentration $$x$$?

Accepted Answer

$$x = 11$$ grams/liter

Question 7

If the equation $$\frac{2x - 1}{x + 3} = -9$$ models the ratio of reactants in a chemical reaction, what is the value of $$x$$?

Accepted Answer

$$x = -\frac{28}{11}$$

Question 8

A medical dosage formula is given by $$\frac{x + 1}{x + 4} = 3. $$What is the value of $$x$$?

Accepted Answer

$$x = \frac{5}{2}$$

Question 9

Which of the following is the correct first step to solve $$\frac{3x^2$}{2} = 28x - 3$$?

Accepted Answer

Multiply both sides by $$2 to $$clear the denominator.

Question 10

If $$\frac{2x - 3x}{12} = 1 - 4$$, what is the simplified form of the left side?

Accepted Answer

$$\frac{-x}{12}$$

Question 11

A historical population model is given by $$\frac{3x^2$}{2} = 28x - 3. $$What type of equation is this?

Accepted Answer

Quadratic equation

Question 12

Which of the following is a valid step in solving $$\frac{3x + 9}{5} = 12$$?

Accepted Answer

Multiply both sides by $$5$$

Step-by-Step Guidance for Solving Rational and Linear Equations (Intermediate Algebra)

Study Guide - Practice Questions