Eighth Grade · Math · week 2

Variables on both sides

Solve linear equations with the variable on both sides by gathering variable terms on one side first.

An equation is a balance: whatever the left side weighs, the right side weighs the same. When x shows up on BOTH sides, the first move is to gather all the x-terms onto one side (by adding or subtracting an x-term from both sides), which turns it back into the one-sided equations from last week.

A smart shortcut: subtract the SMALLER x-term from both sides, so the x-coefficient that remains stays positive. It is not required, but it saves you from juggling extra negative signs.

📋 For the teacher
Teach it (10–15 min):
  • Re-use the balance-scale picture from equation-solving, but now both pans have x-terms on them.
  • Model the shortcut of subtracting the smaller x-term so the remaining coefficient stays positive -- in 2x + 15 = 8x - 3, subtract 2x, not 8x.
  • Insist on checking the answer in BOTH original expressions, not just one -- that is the real proof it works.
  • Connect this to something concrete: comparing two people's money, or two phone plans, where "when are these equal" is exactly this kind of equation.
Talk about it:
  • In 2x + 15 = 8x - 3, why might you subtract 2x from both sides instead of 8x?
  • What does it mean about two people's money when their expressions are set equal?
  • How do you check an answer when x appears on both sides of the original equation?

Mastery looks like: They gather variable terms on one side (choosing the direction that avoids a negative coefficient), solve, and verify in both original expressions.

Common stumbles: Subtracting an x-term from only one side of the equation; ending up with a negative coefficient and mishandling the division step.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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