# Solving for x

This lesson contains three parts that will present
practice problems

and videos to show you how to solve for x .

**Part I **

looks at solving first degree equations, and

indicates that in solving any equation, three

outcomes are possible:

• There is a unique solution(s)

• There is NO solution. This will happen if you

write an illogical equation.

• There are an infinite number of solutions .

When this happens, the equation is called an

identity.

**Part II** looks at solving second degree equations

**Part III** looks at using Excel’s Solver to solve
various

equations (future lesson)

**Definition of Degree**

The degree of an equation is equal to the largest exponent
of the variables in

the equation. It indicates the maximum number of solutions an equation can

have, and it assumes that all exponents are positive integers . For example,

x + 3 is a **first** degree equation. It can have at most

**one** solution.

x^{2} - 8x = 12 is a **2 ^{nd}** degree equation. It can have at
most

**two**solutions.

**Part I: Steps to Solve a First Degree Equation ->**

**Part I: Steps to Solve for X, Working with a First Degree
Equation**

**Step 1** If fractions are present, determine the ** Least
Common
Denominator **. Multiply both sides by the

**LCD .**

**Step 2** Simplify both sides.

**Step 3** Move all terms with x to the left side; move
everything

else to the right side. We can move terms from side to

side by changing the sign of the term .

**Step 4 **Simplify both sides.

**Step 5 **Divide both sides by the coefficient of x.

**Practice Problem #1A: Solving First Degree Equations**

2. 5x + 7 - 2(3 - x) = 2x + 4 - 12

**Answers to Practice Problem #1A: Solving First Degree
Equations**

1. x = 10

2.

3. x = no solution

**Part II: Steps to Solve a Second Degree Equation (x ^{2} -
3x = 10)**

These steps and the Quadratic Formula below will be
discussed in the

video that follows.

**Step 1** If fractions are present, determine the
** Least Common
Denominator**. Multiply both sides by the

**LCD.**

**Step 2** Move everything to the left side. The right
side must be 0.

**Step 3** Simplify the left side, and if possible,
rewrite it in

completely factored form . If it does not factor, use the

Quadratic formula .

**Step 4 **Using the logic, that when the product of
two numbers

equals 0, then one of the numbers must be 0. Rewrite the

problem to create two first degree equations.

**Step 5** Solve the two first degree equations.

**Quadratic Formula**

To solve ax^{2} + bx + c = 0

we use the **Quadratic Formula**

**In the video, we solve this problem:**

Given that: x = Number of calculators to produce

P(x) = Profit made on calculators produced

P(x) = -.4^{2} + 40x - 640

How many calculators must be produced to break even?

**Practice Problem #2A: Solving Second Degree Equations**

1. x^{2} - 6x = 16

2. 2x^{2} - 14x - 36 = 0

3. x^{2} + 6x - 5 = 0

Use a calculator.

**Answers to Practice Problem #2A: Solving Second Degree
Equations**

1. x = 8 or x = -2

2. x = 9 or x = -2

3.

Using a calculator,

**Part III: Future Lesson on Using Excel’s Solver**

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