Exam 1: Equations and Inequalities

Solve the problem. -Jill is 10 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2 kilometers per hour. They meet in 2 hours. How fast is Joe walking?

Solve the problem. -The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater than 1.

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $\text { 10x + } 10 = 2 ( 3 x - 3 )$

Solve the problem. -Find the length of a rectangular lot with a perimeter of $132 \mathrm {~m}$ if the length is $8 \mathrm {~m}$ more than the width.

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 4 x ^ { 2 } + 4 \right| > 0$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ has the given numbers as solutions. Then use those values to write a quadratic equation. - $29 \mathrm { i } , - 29 \mathrm { i }$

Solve the problem. -The area of a square is numerically 60 more than the perimeter. Find the length of the side.

Indicate whether the statement is true always, sometimes, or never. -The product of a pair of complex conjugates (with b ≠ 0) is the difference of the squares of the real and imaginary parts.

Solve the problem. -A real estate development consists of home sites that range in width from 53 to 119 feet and in depth from 140 to 194 feet. Using $x$ as the variable in both cases, write absolute value inequalities that correspond to these ranges.

Determine whether or not the equation is linear. - $0.06 x ^ { 2 } - 0.07 x = 0.90$

Solve the inequality. Write the solution set in interval notation. - $( x + 8 ) ( x - 7 ) ( x - 10 ) < 0$

Solve the inequality. Write the solution set in interval notation. - $| x + 9 | \leq 0$

Solve the equation. - $\frac { 3 } { x + 3 } + \frac { 8 } { x + 6 } = \frac { 10 } { x ^ { 2 } + 9 x + 18 }$

Graph the solution set. - $| x | = - 6$

Decide whether or not the equations are equivalent. -4x - 4 = 9 -4x - 4 = 9

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $\sqrt { - 7 }$

Solve the equation. - $1 - \frac { 5 } { x } - \frac { 24 } { x ^ { 2 } } = 0$

Answer the question. -If a rectangle is $x$ feet long and $y$ feet wide, which one of the following expressions is the length of its diagonal in terms of $x$ and $y$ ?

Solve the problem. -A rectangular enclosure must have an area of at least $4200 \mathrm { yd } ^ { 2 }$ . If $260 \mathrm { yd }$ of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Solve the problem. -Find two consecutive odd integers whose product is 3 .