MOSTMATHHome

Chapter 6 · Equations · page 33 of 68

Simplify each side first

levelAlgebra 1
standard8.EE.C.7
practiceMulti-step equations

Before moving anything across the equals sign, tidy each side on its own. Distribute to remove parentheses and combine like terms. A long equation almost always shrinks to a two-step one.

How to use it

  1. Distribute any number in front of parentheses, including the sign.
  2. Combine like terms on each side separately.
  3. Now collect variables on one side, numbers on the other, and divide.

Example

3(x+2)−4=11⇒3x+2=11⇒x=33(x + 2) - 4 = 11 \Rightarrow 3x + 2 = 11 \Rightarrow x = 3
7n−5n−11=−19⇒2n=−8⇒n=−47n - 5n - 11 = -19 \Rightarrow 2n = -8 \Rightarrow n = -4
−5(x+4)=2(x−4)⇒−5x−20=2x−8⇒−7x=12⇒x=−127-5(x+4) = 2(x-4) \Rightarrow -5x - 20 = 2x - 8 \Rightarrow -7x = 12 \Rightarrow x = -\frac{12}{7}

Where it goes wrong

  • Distributing to the first term only.
  • Combining terms across the equals sign as if it were not there.
  • Panicking at a fraction answer. Equations do not owe you a whole number.

Related

The distributive propertyLike termsVariables on both sides
Practice this