91Ó°ÊÓ

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).

Your local electronics store is having an end-of-the-year sale. The price on a plasma television had been reduced by \(30 \%\). Now the sale price is reduced by another \(30 \% .\) If \(x\) is the television's original price, the sale price can be modeled by $$(x-0.3 x)-0.3(x-0.3 x)$$ a. Factor out \((x-0.3 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(30 \%\) reduction followed by a \(30 \%\) reduction, is the television selling at \(40 \%\) of its original price? If not, at what percentage of the original price is it selling?

Use Einstein's special-relativity equation $$ R_{a}=R_{f} \sqrt{1-\left(\frac{v}{c}\right)^{2}} $$ described in the Blitzer Bonus on page \(44,\) to solve this exercise. You are moving at \(90 \%\) of the speed of light. Substitute \(0.9 c\) for \(v,\) your velocity, in the equation. What is your aging rate, correct to two decimal places, relative to a friend on Earth? If you are gone for 44 weeks, approximately how many weeks have passed for your friend?

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. A number decreased by the difference between eight and the number

Solve each equation. $$\begin{array}{r} 25-[2+5 x-3(x+2)]= \\ -3(2 x-5)-[5(x-1)-3 x+3] \end{array}$$

Describe ways in which solving a linear inequality is different than solving a linear equation.

Solve each equation. $$10 x-1=(2 x+1)^{2}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set, I should obtain a true statement, and when 0 does not belong to the solution set. I should obtain a false statement.

You had \(\$ 10,000\) to invest. You put \(x\) dollars in a safe, government- insured certificate of deposit paying \(5 \%\) per year. You invested the remainder of the money in noninsured corporate bonds paying \(12 \%\) per year. Your total interest earned at the end of the year is given by the algebraic expression $$ 0.05 x+0.12(10,000-x) $$ a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested \(\$ 6000\) in the safe, government-insured certificate of deposit.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In an inequality such as \(5 x+4<8 x-5,\) I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.