Download Math 110 – Sections 2.1-2.3 2.1 Simplifying Algebraic Expressions

2.1 Simplifying Algebraic Expressions
Term – a number or the product of a number and
variables raised to power.
Math 110 – Sections 2.1-2.3
Numerical coefficient of a term is the numerical factor.
Example 1. Identify the numerical coefficient in each term.
Combining like terms:
- Simplifying the sum or difference of like terms.
• Like terms – have the same variables raised
to the same power
• Unlike terms – not like terms
Example 3. Simplify each by combining like terms.
a) 8 y − 12 y
b) 13z 2 + 5z 2
c) 6 y − 3 x + 7 x
Example 2. Determine whether the terms are like or unlike.
a) 2 x, − 6 x
b) 3 x 2 y 2 , -x 2 y 2 , 4 xy
c) − 5ab, 6ba
Note: In combining like terms, we can simply add numerical
coefficients and multiply by common variable factors.
Example 4. Simplify by combining like terms.
a) − 7 xy − 2 + x + 3
b) 4z 2 − 5z
c) −
1
x + 2x
4
Example 5. Find each product using the distributive
property to remove parentheses.
Removing parentheses by using the distributive
property.
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Example 6. Simplify the following expressions.
a) 4( x − 2) − 3 x + 5
c) 9 − 5(6 y − 3)
b) 3(2 x + 1) − (5 x − 2 )
Example 7. Write the following phrases as
algebraic expressions and simplify if possible.
a) Three times a number subtracted from 10
b) Five added to twice the sum of a number and
seven.
2.2 Addition and Multiplication
Properties of Equality
Example 1. Solve for x.
Linear Equation in one variable:
Example 2. Solve for y.
Addition Property of an Equality.
Example 3. Solve for x.
Multiplication Property of Equality
We can multiply (or divide) both sides of an equation by any
nonzero real number and the solution does not change.
Example 5. Solve for x.
Example 4. Solve:
2
Example 6. Solve for x.
Writing Algebraic Expressions
Example 9.
a) The sum of two numbers is 50. If one number is x,
write an expression representing the other.
b) If x is the first of three consecutive integers, express the
sum of the three integers in terms of x. Then simplify.
Example 7. Solve for x.
2.3 Solving Linear Equations
Example 1. Solve:
1. Multiply both sides by the LCD to clear the equations
of fractions if they occur.
2. Use the distributive property to remove parentheses.
3. Simplify each side of the equation by combining like
terms.
4. Get all variable terms on one side and all numbers
on the other side using the addition property.
5. Get the variable alone by using the multiplication
property.
6. Check the solution by substituting it into the original
equation.
Example 2. Solve:
Example 3. Solve:
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Example 4. Solve:
Example 5. Solve:
Example 6. Solve:
Example 7. Three times a number, subtracted from
two, equals twice the number, added to twenty seven.
Find the number.
0.06 x − 0.10(x − 2 ) = −0.02(8)
− 6(2 x + 1) − 14 = −10( x + 2) − 2 x
5(2 − x ) + 8 x = 3(x − 6)
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