91Ó°ÊÓ

Solve each equation for the indicated variable. \(\frac{y-a}{b}=\frac{x+b}{c}\) for \(x\)

Solve each inequality and express the solution set using interval notation. \(-5 x-2<-14\)

Use an algebraic approach to solve each problem. Suppose that the width of a certain rectangle is 1 inch more than one-fourth of its length. The perimeter of the rectangle is 42 inches. Find the length and width of the rectangle.

Solve each equation. \(3(x-4)-7(x+2)=-2(x+18)\)

Use an algebraic approach to solve each problem. Eva invested a certain amount of money at \(4 \%\) interest and 1500 dollars more than that amount at \(6 \%\). Her total yearly interest was 390 dollars. How much did she invest at each rate?

For Problems \(35-44\), solve each compound inequality and graph the solution sets. Express the solution sets in interval notation. $$ 5 x-2<-2 \text { or } 5 x-2>2 $$

Use an algebraic approach to solve each problem. Suppose that the width of a rectangle is 3 centimeters less than two-thirds of its length. The perimeter of the rectangle is 114 centimeters. Find the length and width of the rectangle.

Solve each equation. \(4(x-2)-3(x-1)=2(x+6)\)

Solve each inequality. $$ |7 x-6| \geq 22 $$

Use an algebraic approach to solve each problem. A total of 4000 dollars was invested, part of it at \(5 \%\) interest and the remainder at \(6 \%\). If the total yearly interest amounted to 230 dollars, how much was invested at each rate?