1. Equations & Inequalities

Solve each equation in Exercises 83–108 by the method of your choice. $2x^2-7x=0$

Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 2) = 1/3

In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x² - 4x - 5

In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = - (x + 1)² + 4

Find all values of x satisfying the given conditions. y = 5x² + 3x and y = 2

Find all values of x satisfying the given conditions. y₁ = 2x² + 5x - 4, y₂ = - x² + 15x - 10, and y₁ - y₂ = 0

Find all values of x satisfying the given conditions. y₁ = - x² + 4x - 2, y₂ = - 3x² + x - 1, and y₁ - y₂ = 0

When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Use specific values for x and y to show that, in general, 1/x + 1/y is not equivalent to 1 / x + y.

Solve each equation by the square root property. $\frac{x^2}{2}+5=-3$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x^2+20x$

Solve each equation by completing the square. $3x^2-12x+11=0$

Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)²