Alegebra 1study Cheet Sheet

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Kyle Ferguson

3.1: Solve One-Step Equations

X/5=14 (Write original equation)
X/5 x 5=14 x 5 (Multiply each side by 5)
14 x 5 (Solve)
X = 70 (Simplify, variable first)
Make sure to check the equation every time!
Make sure to show the inverse operations!

3.2: Solve Two-Step Equations

4x-9=3 (Write original equation)
4x-9+9=3+9 (Add nine to each side of the equation)
4x=12 (Simplify)
4x/4=12/4 (Divide by four on each side of the equation)
X=3 (Simplify)

3.3: Solve Multi-Step Equations

5x-2(4x+3)=9 (Write original equation)
5x-8x-6+9 (Distributive Property)
-3x-6=9 (Combine like terms)
-3x=15 (Add 6 to each side of the equation)
X=-5 (Divide each side of the equation by -3)

3.4: Solve Equations with Variables On Each Side Of The Equation

-2(x-5)=7-2x (Write original equation)
-2x+10=7-2x (Distributive Property)
-2x+3+-2x (Subtract seven from each side)
Now you have to add two to both sides.
Finally you are left with 3=0.
Three does not equal zero so the answer is NO REAL SOLUTION!

3.5: Write Ratios And Proportions

Make proportions so that you can solve for x.
88 x 5/20=88 x x/88 (Multiply each side by 88)
X=22 (Simplify, with the variable in front of the constant)

3.6: Solve Proportions Using Cross Products

3/10 = 12/x (Write original equation)
3 x x=10 x 12 (Cross products property)
3x=120 (Simplify)
X=40 (Divide each side by 3)

3.7: Solve Percent Problems

42 is 40% of what number? (Write original equation)
A=p% x b (Write percent equation)
42=40% x b (Substitute 42 for a and 40 for p)
42=0.4 x b (Write percent as a decimal)
10b=b (Divide each side by 0.4)

3.8: Rewrite Equations And Formulas

Write 5x+4y-7=5 so that y is a function of x.
5x+4y-7=5 (Write original equation)
5x+4y=12 (Add 7 to each side of the equation)
4y=12-5x (Subtract 5x from each side of the equation)
Y=3- 5/4x (Divide each side by 4)
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