Q: Which of the following pairs of equations are equivalent?

$$2x + 3 = 5$$ \text{ and } x = 1$

Question 1

Which of the following is the definition of a linear equation in one variable?

Accepted Answer

An equation that can be expressed in the form $$mx + b = 0$$, where $$m$$ and $$b$$ are real numbers and $$m 
eq 0.$$

Question 2

Given the equation $$3x - 7 = 2x + 5$$, what is the solution for $$x$$?

Accepted Answer

$$x = 1$$

Question 3

Which of the following pairs of equations are equivalent?

Accepted Answer

$$2x + 3 = 5$$ 	ext{ and } x = 1$

Question 4

If $$a = b is $$true, which of the following is always true according to the Addition Principle?

Accepted Answer

$$a + c = b + c$$

Question 5

Solve the equation $$\dfrac{3}{4}x - 1 = \dfrac{7}{5}$$ for $$x.$$

Accepted Answer

$$x = \dfrac{16}{5}$$

Question 6

Which of the following equations has no solution?

Accepted Answer

$$-24x + 7 = 17 - 24x$$

Question 7

Which equation has infinitely many solutions?

Accepted Answer

$$3 - \dfrac{1}{3}x = -\dfrac{1}{3}x + 3$$

Question 8

A car travels at a constant speed of 60 mph. How far will it travel in 2.5 hours?

Accepted Answer

$$150$$ miles

Question 9

A train leaves a station traveling at 80 mph. Two hours later, a second train leaves the same station traveling at 100 mph. How long after the second train leaves will it overtake the first train?

Accepted Answer

Question 10

A student borrows $$P$$ dollars at a simple interest rate $$r$$ for $$t$$ years. Which formula gives the total interest $$I$$ paid?

Accepted Answer

$$I = Prt$$

Question 11

Damarion has two student loans totaling $$28,000. $$One loan is at $$5\%$$ simple interest, the other at $$3\%. $$After one year, he owes $$1,040 in $$interest. How much did he borrow at $$5\%$$?

Accepted Answer

$$10,000$$

Question 12

Find the zero of the linear function $$f(x) = 5x - 9.$$

Accepted Answer

$$x = 1.8$$

Question 13

Which of the following best describes the solution set of $$x + 2 = x + 2$$?

Accepted Answer

All real numbers

Question 14

If $$f(x) = mx + b$$ and $$m 
eq 0$$, what is the formula for the zero of $$f$$?

Accepted Answer

$$x = -\dfrac{b}{m}$$

Question 15

A company models its profit $$P as a $$linear function of the number of units sold $$x$$: $$P(x) = 12x - 300. $$How many units must be sold for the company to break even?

Accepted Answer

$$25$$

Question 16

Which of the following is NOT a step in the recommended problem-solving process for applied linear models?

Accepted Answer

Ignore unknowns and focus only on known facts.

Question 17

If $$f(x) = 7x + 2$$, what is the value of $$x$$ for which $$f(x) = 0$$?

Accepted Answer

$$x = -\dfrac{2}{7}$$

Question 18

A cyclist travels at 15 mph for $$t$$ hours. Write an equation for the distance $$d$$ traveled and find $$t if$$ $$d = 45$$ miles.

Accepted Answer

$$d = 15t$$, $$t = 3$$

Question 19

Which of the following is a correct application of the Multiplication Principle?

Accepted Answer

If $$a = b$$, then $$ac = bc$$ for any real number $$c.$$

Linear Equations, Functions, Zeros, and Applications – Precalculus Study Notes

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