Q: Which of the following is a property of inequalities that differs from equations?

Multiplying both sides by a negative number reverses the inequality

Question 1

Which of the following is a linear equation in the variables $x$ and $y$?

Accepted Answer

$x + 3y = 7$

Question 2

Solve the linear equation $\frac{2}{5}x = 6$ for $x$.

Accepted Answer

$x = 15$

Question 3

A trader sells some units of a product at $6 per unit and the rest at $8 per unit. If he sells 100 units in total and receives $660, how many units did he sell at $8 per unit?

Accepted Answer

$30$

Question 4

Which of the following statements about linear equations is TRUE?

Accepted Answer

A linear equation has all variables with exponent one.

Question 5

Given the system of equations: $x + y = 3$ and $5x - 5y = 1$, what is the value of $x$?

Accepted Answer

$x = 1.6$

Question 6

If the sum of incomes of A and B is $2640 and B's income is 20% more than A's, what is B's income?

Accepted Answer

$1440$

Question 7

Solve the inequality $2x + 1 \leq 6x - 1$.

Accepted Answer

$x \geq \frac{1}{2}$

Question 8

Which transformation does NOT produce an equivalent inequality?

Accepted Answer

Multiplying both sides by a negative number without reversing the inequality

Question 9

A function $f(x)$ is defined as $f(x) = 3x + 1$. What is $f(4)$?

Accepted Answer

$13$

Question 10

Which of the following is NOT a function?

Accepted Answer

$y^2 = x$

Question 11

The demand function for a product is $q = 600 - 8p$. What is the quantity demanded when the price is $p = 32$?

Accepted Answer

$q = 352$

Question 12

Which of the following best describes the graph of a quadratic function $f(x) = ax^2 + bx + c$ where $a > 0$?

Accepted Answer

A parabola opening upwards

Question 13

In linear programming, what is the feasible region?

Accepted Answer

The region that satisfies all the constraints

Question 14

Given the constraints $4x + 2y \leq 60$ and $2x + 4y \leq 48$, which of the following is a valid intercept for the first constraint?

Accepted Answer

$(x=0, y=30)$

Question 15

A company wants to maximize profit $Z = 6500x + 4500y$ subject to $4x + 2y \leq 60$ and $2x + 4y \leq 48$. What is the optimal number of tables ($x$) and chairs ($y$) to produce?

Accepted Answer

$x = 12, y = 6$

Question 16

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each element in the domain is paired with only one element in the range

Question 17

Solve the compound inequality $-2 < 3t - 8 < 10$.

Accepted Answer

$2 < t < 6$

Question 18

If the supply function is $S = -a + bP$ and the demand function is $D = a - bP$, what is the equilibrium price $P$?

Accepted Answer

$P = \frac{a}{b}$

Question 19

Which of the following is a property of inequalities that differs from equations?

Accepted Answer

Multiplying both sides by a negative number reverses the inequality

Question 20

Given the function $f(x) = 2x + 5$, what is the range of $f(x)$?

Accepted Answer

All real numbers $y$

Equations, Inequalities, and Functions: College Algebra Study Notes

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