Summary Math Equation Solving in SAT--Time Saving

Solving Equations—Quick Reference
Integer Rules Distributive Property Examples
Addition: 3(x+5) = 3x +15 Multiply the 3 times x and 5.
• If the signs are the same, add the numbers
and keep the sign. -2(y –5) = -2y +10 Multiply –2 times y and –5.
• If the signs are different, subtract the num-
5(2x –6) = 10x –30 Multiply 5 times 2x and –6.
bers and keep the sign of the number with
the largest absolute value.
Solving Equations Study Guide
1. Does your equation have fractions?
Subtraction: Add the opposite Yes—Multiply every term (on both sides) by the
Keep—Change—Change denominator.
• Keep the first number the same. No—Go to Step 2.
• Change the subtraction sign to addition.
2. Does your equation involve the distributive property?
• Change the sign of the second number to
(Do you see parenthesis?)
it’s opposite sign. Yes—Rewrite the equation using the distributive
property.
Multiplication and Division: No—Go to Step 3.
• If the signs are the same, the answer is 3. On either side, do you have like terms?
positive. Yes—Rewrite the equation with like terms
• If the signs are different, the answer is together. Then combine like terms.
negative. (Don’t forget to take the sign in front of each
term!)
No– Go to Step 4.

4. Do you have variables on both sides of the equation?
Golden Rule for Solving Equations: Yes—Add or subtract the terms to get all the
variables on one side and all the constants
on the other side. Then go to step 6.
Whatever You Do To One Side of the No—Go to Step 5.
Equation, You Must Do to the Other
5. At this point, you should have a basic two-step
Side! equation. If not go back and recheck your steps
above.
- Use Addition or Subtraction to remove any
constants from the variable side of the equation.
Combining Like Terms
(Remember the Golden Rule!)

Like terms are two or more terms that contain 6. Use multiplication or division to remove any
the same variable. coefficients form the variable side of the equation.
(Remember the Golden Rule!)
Example: 3x, 8x, 9x are like terms. 7. Check your answer using substitution!
2y, 9y, 10y are like terms.

3x, 3y are NOT like terms Congratulations! You are finished the
because they do problem!
NOT have the
same variable!

, Graphing Equations—Quick Reference

Slope= rise Graphing Using Slope Intercept
run Form
1. Identify the slope and y-intercept in the
• Calculate the slope by choosing two points equation.
on the line. y = 3x -2
• Count the rise (how far up or down to get
Slope Y-intercept
to the next point?) This is the numerator.
• Count the run (how far left or right to get to 2. Plot the y-intercept on the graph.
the next point?) This is the denominator.
•Write the slope as a fraction.




3. From the y-intercept, count the rise and
run for the slope. Plot the second point.




Slope = 3/5

** Read the graph from left to right. If the line is
falling, then the slope is negative. 4. Draw a line through your two points.
If the line is rising, the slope is positive.

**When counting the rise and run, if you count down
or left, then the number is negative. If you count
up or right, the number is positive.

Slope Intercept Form
y = mx +b

Slope Y-intercept