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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

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Solving Equations

Wed 16 Sep — A.6 Solving Equations

Solving Equations:

Equation is two expressions set equal to each other.

To solve an equation means to find the values of the
variables in their domains that make the equation a
true statement. A solution satisfies an equation.

3 types of equations: Conditional, identity, contradiction
(Give Examples of each)

Solve these:

Solve:

Use the standard procedure. Ans: –3

We can also solve this graphically. Since we want the value of x that makes these two expressions
equal, we could graph each and see where they intersect.

Rewrite this as follows:

Find value of x where f(x) = g(x) on the graph:

Solve:

Note how graphs are parallel lines. No soln.

Solve:

Solve:

Solve:

Solve:

Solve:

We can also solve a quadratic equation by Completing
the Square. All that means is that we construct a
perfect square from a given expression and then use
the square root method to solve.

To complete the square of take half of b,
square this, and then add it to the expression.
For example, to make a perfect square we add

We get which can be written , a perfect square.

Solve by completing the square:

Solve by completing the square:

The standard form of a quadratic equation:

where a, b, c are real numbers
and a is not 0.

We can use completing the square to solve this
to get the quadratic formula:

Solve using quadratic formula:

Solve:

Solve: