91Ó°ÊÓ

Determine whether the following statements are true or false. The equation \((3 x+1)^{2}=16\) has the same solution set as the equation \(3 x+1=4\).

Determine whether each statement is true or false. Assume that \(a\) is a positive real number. If \(x < a,\) then \(a > x\)

Solve the absolute value equation. $$5|y-2|-10=4|y-2|-3$$

Monthly Driving Costs. The monthly costs associated with driving a new Honda Accord are the monthly loan payment plus \(\$ 25\) every time you fill up with gasoline. If you fill up 5 times in a month, your total monthly cost is \(\$ 500 .\) How much is your loan payment?

Determine whether the following statements are true or false. The quadratic equation \(a x^{2}+b x+c=0\) can be solved by the square root method only if \(b=0\).

Solve the absolute value equation. $$3-|y+9|=11-3|y+9|$$

Determine whether each statement is true or false. Assume that \(a\) is a positive real number. $$\text { If }-x \geq a, \text { then } x \geq-a$$

100\. Budget: Monthly Driving Costs. The monthly costs associated with driving a Ford Explorer are the monthly loan payment plus the cost of filling up your tank with gasoline. If you fill up 3 times in a month, your total monthly cost is \(\$ 520 .\) If you fill up 5 times in a month, your total monthly cost is \(\$ 600 .\) How much is your monthly loan, and how much does it cost every time you fill up with gasoline?

Solve the absolute value equation. $$\left|4-x^{2}\right|=1$$

Determine whether the following statements are true or false. All quadratic equations can be solved exactly.