MOSTMATHHome

Chapter 9 · Questions · page 61 of 68

How do you solve an equation with x over a number?

Short answerClear the added or subtracted number first, then multiply both sides by the denominator. For x/4 + 3 = 7, subtract 3 to get x/4 = 4, then multiply by 4 to get x = 16.

levelPre-algebra
standard7.EE.B.4a
practiceOne- and two-step equations

x/4 means x divided by 4, and the opposite of dividing by 4 is multiplying by 4. Same reverse-order idea as any two-step equation, with multiplication as the last move.

How to use it

  1. Subtract or add on both sides to get the fraction alone.
  2. Multiply both sides by the denominator.
  3. Check by substituting.

Example

x4+3=7⇒x4=4⇒x=16\frac{x}{4} + 3 = 7 \Rightarrow \frac{x}{4} = 4 \Rightarrow x = 16
n3−5=−2⇒n3=3⇒n=9\frac{n}{3} - 5 = -2 \Rightarrow \frac{n}{3} = 3 \Rightarrow n = 9

Where it goes wrong

  • Stopping at x/4 = 4 and answering 4.
  • Dividing by 4 instead of multiplying.

Related

Two-step equationsUndo in reverse order
Practice this