Chapter 2

Solve each inequality and express the solution set using interval notation. \(-2(x-4)<5(x-1)\)

Solve \(i=\) Prt for \(r\), given that \(i=\$ 159.50, P=\$ 2200\), and \(t=0.5\) of a year. Express \(r\) as a percent.

Solve each equation. \(|x+1|=|x-4|\)

Give a step-by-step description of how you would solve the inequality \(-3>5-2 x\).

Do the less than and greater than relations possess a symmetric property similar to the symmetric property of equality? Defend your answer.

Solve \(A=P+\) Prt for \(P\), given that \(A=\$ 1423.50\), \(r=9 \frac{1}{2} \%\), and \(t=1\) year.

Use an algebraic approach to solve each problem. Make up an equation whose solution set is the set of all real numbers and explain why this is the solution set.

Solve each equation. \(|x+1|=|x-1|\)

How would you explain to someone why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number?

Use an algebraic approach to solve each problem. Solve each of the following equations. (a) \(5 x+7=5 x-4\) (b) \(4(x-1)=4 x-4\) (c) \(3(x-4)=2(x-6)\) (d) \(7 x-2=-7 x+4\) (e) \(2(x-1)+3(x+2)=5(x-7)\) (f) \(-4(x-7)=-2(2 x+1)\)

Use an algebraic approach to solve each problem. Verify that for any three consecutive integers, the sum of the smallest and largest is equal to twice the middle integer. [Hint: Use \(n, n+1\), and \(n+2\) to represent the three consecutive integers.]

Use an algebraic approach to solve each problem. Verify that no four consecutive integers can be found such that the product of the smallest and largest is equal to the product of the other two integers.