Solve the equation $5x-9=3x-5.$

Solve the equation ${\displaystyle \frac{7}{24}}={\displaystyle \frac{x}{8}}+{\displaystyle \frac{1}{6}}.$

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

The width of a rectangle is 3 centimeters less than the length, and the area is 54 square centimeters. Find the dimensions of the rectangle.

Solve the equation $x^2+36=-13x.$

If Fran invests $8200 at 6% per year, how much additional money must she invest at 8% to ensure that the interest she receives each year is 7% of the total investment?

A frame of uniform width borders a painting that is 25 inches long and 11 inches high. If the area of the framed picture is 351 square inches, find the width of the border.

Solve $-6x-15={(2x+5)}^2.$

Determine the constant that should be added to the binomial

so that it becomes a perfect-square trinomial. Then write and factor the trinomial.

Solve $3x^2-5x-1=0.$

A box with a square base and no top is made from a square piece of cardboard by cutting 2-inch squares from each corner and folding up the sides. What length of side must the original cardboard square have if the volume of the box is 50 cubic inches?

Solve $x^2+12x+33=0.$

Solve the polynomial equation

by factoring and then using the zero-product property.

Solve the equation

by making an appropriate substitution.

Solve the absolute value equation

${\displaystyle \frac{x}{2}}-5\ge {\displaystyle \frac{4x}{9}}$

$-4<2x-3<4$

Solve the inequality

by first rewriting it as an equivalent inequality without absolute value bars. Express the solution set in interval notation.

Solve the linear inequality ${\displaystyle \frac{2}{5}}y-13\le -(7+{\displaystyle \frac{13}{5}}y).$

Solve the inequality $0\le 5x-2\le 8.$