Final answer:
When solving linear equations, isolate the variable. When factoring quadratic expressions, use binomial multiplication. When finding roots of polynomials, set the polynomial equal to zero. When graphing linear inequalities, indicate the solution on a number line or coordinate plane.
Step-by-step explanation:
When solving linear equations, the goal is to isolate the variable on one side of the equation. This is done by adding, subtracting, multiplying, and dividing both sides of the equation by the same values. Here's an example:
Example:
- 2x + 5 = 13
- Subtract 5 from both sides: 2x = 13 - 5 = 8
- Divide both sides by 2: x = 8/2 = 4
When factoring quadratic expressions, the goal is to write the expression as a product of two binomials. Here's an example:
Example:
- x^2 + 5x + 6
- Find two numbers that multiply to 6 and add to 5: 2 and 3
- Write the expression as a product: (x + 2)(x + 3)
When finding roots of polynomials, you are finding the values of the variable that make the polynomial equal to zero. This can be done by factoring or using the quadratic formula.
When graphing linear inequalities, you can use a number line or a coordinate plane. The solution includes all the points that satisfy the inequality. The boundary line is dotted if the inequality is not strict, and solid if it is strict.