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May 20th

May 20th

# Solving Linear and Quadratic Equations and Absolute Value Equations

Slide 1 Session 3
and Absolute Value Equations
Slide 2 Solving Equations

An equation is a statement ex pressing the equality of two
mathematical expressions . It may have numeric and variable terms
on the left hand side (LHS) and similar terms on the right hand
side (RHS):

LHS = RHS

3x + 2 = 27x − 4

We want to solve the equation, which means we want to get the
variable by itself on the left side and the numeric values by
themselves on the right side, if possible.
Slide 3 Solving Equations

Solving an equation means finding the value(s) the variable can
take on to make the equation a true statement. Sometimes there
are no such values:

x = x + 1

Sometimes there are multiple solutions:

x2 = 4

This equation has two solutions : 2 and -2.
Slide 4 Solving Linear Equations

To solve linear equations, we can use the additive and
multiplicative
properties of equality .

If a = b, then a + c = b + c.

If we choose c to be the additive inverse of a term, we can add or
subtract it from both sides of the equation, and take steps to
isolate
the variable term.

3 + x = 5
3 − 3 + x = 5− 3
x = 2

Slide 5 Solving Linear Equations

The multiplicative property of equality:

If a = b, then ac = bc

If we choose c to be the multiplicative inverse of a term, we can
multiply both sides of the equation by the multiplicative inverse
and “get rid of” or ”divide out” a coefficient on the variable we are
trying to isolate.

Slide 6 Steps in Solving Linear Equations

1. Remove all parentheses by using the distributive property .

2. Use the additive property of equality to move all variable terms
to the LHS and all constant terms to the RHS.

3. Simplify by combining like terms .

4. Use the multiplicative property of equality to change the
coefficient of the variable to 1.

5. Simplify the RHS. When the variable is al one on the LHS , the
RHS is the solution to the equation.

original equation. (Always!)
Slide 7 Example: Solving Linear Equations

 Distributive property Combine like terms Add 2x to each side Combine like terms Add 3 to each side Combine like terms Multiply each side by This is the solution Check your answer Yes!
Slide 8 Finding Linear Equations

If you know two points, (the x and y coordinates of the
first
point) and (the x and y coordinates of the second
point), you can find the equation for a line:

1. The slope is the change in y divided by the change in x:

2. Set up a formula in the standard form, using the slope you
calculated

y = mx + b

3. Substitute x and y values for one of the points and solve for b

4. Check your answer using the x and y values for the other point
(Always!)

Slide 9 Example: Find the Equation for a Line

Suppose you have two points (-1,0) and (2,6) and you want to find
the equation for the line through those two points.

Slide 10 Example: Find the Equation for a Line

1. The slope is the change in y divided by the change in x:

2. Set up a formula in the standard form, using the slope you
calculated

y = 2x + b

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