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Chapter 6 · Equations · page 30 of 68

When the x term is negative

levelGrade 7
standard7.EE.B.4
practiceTwo-step equations

In 10 − 2x = 4, the x term is −2x. The minus belongs to it. You can divide by −2 at the end, remembering the sign flips, or add 2x to both sides first so you never divide by a negative at all.

How to use it

  1. Either: isolate −2x, then divide both sides by −2.
  2. Or: add 2x to both sides, move the numbers, divide by positive 2.
  3. Both give the same answer. The second avoids sign slips.

Example

10−2x=4  ⇒  −2x=−6  ⇒  x=310 - 2x = 4 \;\Rightarrow\; -2x = -6 \;\Rightarrow\; x = 3
10−2x=4  ⇒  10=4+2x  ⇒  6=2x  ⇒  x=310 - 2x = 4 \;\Rightarrow\; 10 = 4 + 2x \;\Rightarrow\; 6 = 2x \;\Rightarrow\; x = 3

Where it goes wrong

  • Dividing −6 by 2 instead of −2 and getting −3.
  • Reading 10 − 2x as (10 − 2)x.

Related

Two-step equationsMultiplying and dividing signsThe sign belongs to the term
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