Download 5-SolveEquationsbyCombineLikeTerms

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5-Solving Equations Combine Like Terms
CC Algebra I
Simplifying and Combining Like Terms
4x2
* Write the coefficients, variables, and exponents of the following:
Coefficients
Variables
Exponents
2
8c
9x
y8
12a2b3
Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)).
When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding
or subtracting the numerical coefficients.
Examples:
3x + 4x = 7x
13xy – 9xy = 4xy
12x3y2 - 5x3y2 = 7x3y2
11x2 – 7x
6x3y + 5xy3
Can you simplify?
4x3 + 4y3
Simplify the following:
1)
7x + 5 – 3x
4)
12x – 5 – 7x – 11
2)
6w2 + 11w + 8w2 – 15w
5) 2x2 - 3x + 7 – 3x2 + 4x – 7
3)
6x + 4 + 15 – 7x
6)
11a2b – 12ab2
13. The perimeter of a rectangle is 24 inches. Find the dimensions if its length is 3 inches greater than its
width.
14. You are visiting Baltimore, MD and a taxi company charges a flat fee of $3.00 for using the taxi and
$0.75 per mile.
A. Write an equation that you could use to find the cost of the taxi ride in Baltimore, MD. Let x
represent the number of miles and y represent the total cost.
B. How much would a taxi ride for 8 miles cost?
C. If a taxi ride cost $15, how many miles did the taxi travel?
15. A plumber charges $50 to make a house call. He also charges $25.00 per hour for labor.
A. Write an equation that you could use to the amount a plumber charges for a house call based on the
number of hours of labor.
B. How much would it cost for a house call that requires 2.5 hours of labor?
C. If the bill from the plumber is $162.50, how many hours did the plumber work at your house?
Aim –How can we solve equations with like terms?
Solve the following equations:
1) 2x  3x  4  19
2) x  2x  5x  5  101
3) 15x  5  25  75
4) x  4x  24
5) 2  3x  3  14
6) 4x  6  2x  14
7) 2  6x  8 14x  66
8) x 10  4x  22  12
9) 2x 12  x  38
10) 5x  6  2x 11  4x  2  0
11) 12x 13  8x  37
12) 7  5x  7  15