Chapter 2

A student in an algebra course has test scores of \(75,82,71\), and 84 . What score on the next test will raise the student's average to 80 ?

Solve the equation. $$-3 x+4=-1$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ (3 x+1)(5-10 x)>0 $$

Given \(-7<-3\), determine the inequality obtained if (a) 5 is added to both sides (b) 4 is subtracted from both sides (c) both sides are multiplied by \(\frac{1}{3}\) (d) both sides are multiplied by \(-\frac{1}{3}\)

Exer. 1-50: Solve the equation. $$ |x+4|=11 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (5-2 i)+(-3+6 i) $$

Exer. 1-14: Solve the equation by factoring. $$ 6 x^{2}+x-12=0 $$

Before the final exam, a student has test scores of \(72,80,65,78\), and 60 . If the final exam counts as one-third of the final grade, what score must the student receive in order to have a final average of \(76 ?\)

Solve the equation. $$2 x-2=-9$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ (2-3 x)(4 x-7) \geq 0 $$

Given \(4>-5\), determine the inequality obtained if (a) 7 is added to both sides (b) \(-5\) is subtracted from both sides (c) both sides are divided by 6 (d) both sides are divided by \(-6\)

Exer. 1-50: Solve the equation. $$ |x-5|=2 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-5+7 i)+(4+9 i) $$

Exer. 1-14: Solve the equation by factoring. $$ 4 x^{2}+x-14=0 $$

A worker's take-home pay is \(\$ 492\), after deductions totaling \(40 \%\) of the gross pay have been subtracted. What is the gross pay?

Solve the equation. $$4 x-3=-5 x+6$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ (x+2)(x-1)(4-x) \leq 0 $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ x<-2 $$

Exer. 1-50: Solve the equation. $$ |3 x-2|+3=7 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (7-6 i)-(-11-3 i) $$

Exer. 1-14: Solve the equation by factoring. $$ 15 x^{2}-12=-8 x $$

A couple does not wish to spend more than \(\$ 70\) for dinner at a restaurant. If a sales tax of \(6 \%\) is added to the bill and they plan to tip \(15 \%\) after the tax has been added, what is the most they can spend for the meal?

Solve the equation. $$5 x-4=2(x-2)$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ (x-5)(x+3)(-2-x)<0 $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ x \leq 5 $$

Exer. 1-50: Solve the equation. $$ 2|5 x+2|-1=5 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-3+8 i)-(2+3 i) $$

Exer. 1-14: Solve the equation by factoring. $$ 15 x^{2}-14=29 x $$

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100 . (a) Find the IQ of a 12-year-old child whose mental age is \(15 .\) (b) Find the mental age of a person 15 years old whose IQ is 140 .

Solve the equation. $$4(2 y+5)=3(5 y-2)$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{2}-x-6<0 $$

Exer. 1-50: Solve the equation. $$ 3|x+1|-2=-11 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (3+5 i)(2-7 i) $$

Exer. 1-14: Solve the equation by factoring. $$ 2 x(4 x+15)=27 $$

Water covers \(70.8 \%\), or about \(361 \times 10^{6} \mathrm{~km}^{2}\), of Earth's surface. Approximate the total surface area of Earth.

Solve the equation. $$6(2 y+3)-3(y-5)=0$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{2}+4 x+3 \geq 0 $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ x>-3 $$

Exer. 1-50: Solve the equation. $$ |x-2|+5=5 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-2+6 i)(8-i) $$

Exer. 1-14: Solve the equation by factoring. $$ x(3 x+10)=77 $$

The cost of installing insulation in a particular two-bedroom home is \(\$ 2400\). Present monthly heating costs average \(\$ 200\), but the insulation is expected to reduce heating costs by \(10 \%\). How many months will it take to recover the cost of the insulation?

Solve the equation. $$\frac{1}{5} x+2=3-\frac{2}{7} x$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{2}-2 x-5>3 $$

Exer. 3-12: Express the inequality as an interval, and sketch its graph. $$ -2

Exer. 1-50: Solve the equation. $$ 9 x^{3}-18 x^{2}-4 x+8=0 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (1-3 i)(2+5 i) $$

Exer. 1-14: Solve the equation by factoring. $$ 75 x^{2}+35 x-10=0 $$

A workman's basic hourly wage is \(\$ 10\), but he receives one and a half times his hourly rate for any hours worked in excess of 40 per week. If his paycheck for the week is \(\$ 595\), how many hours of overtime did he work?

Solve the equation. $$\frac{5}{3} x-1=4+\frac{2}{3} x$$