Solving Equations Worksheets

What does solving an equation mean?

An equation says two expressions are equal. Solving it means finding the value of $x$ that makes the statement true. The method is to keep the equation balanced: whatever you do to one side, do to the other, and undo the operations around $x$ in reverse order until $x$ is alone.

Every solution on these worksheets is a positive whole number, so students can concentrate on the steps.

• Easy — one-step equations: $x + a = b$ or $ax = b$.
• Medium — two-step equations: $ax + b = c$.
• Hard — parentheses, $a(x + b) = c$, or variables on both sides, $ax + b = cx + d$.

Worked examples

Easy: $x + 7 = 12$ and $6x = 42$

Undo the addition by subtracting 7 from both sides: $x = 5$. Undo the multiplication by dividing both sides by 6: $x = 7$.

Medium: $5x + 3 = 38$

Undo the addition first, then the multiplication:

Hard: $7x + 4 = 3x + 24$

Collect the $x$-terms on one side and the numbers on the other:

A Hard problem with parentheses, $3(x + 4) = 27$, can be solved by dividing both sides by 3 first: $x + 4 = 9$, so $x = 5$.

Check your answers

Substitute the solution into the original equation. For $x = 5$: $7(5) + 4 = 39$ and $3(5) + 24 = 39$.

Common mistakes

• Changing only one side. Subtracting 3 from the left of $5x + 3 = 38$ without subtracting it from the right breaks the equation.
• Undoing in the wrong order. Dividing $5x + 3 = 38$ by 5 first is possible but every term must be divided, including the 3; it is easier to subtract first.
• Sign errors when moving terms. Moving $3x$ from the right side to the left makes it $-3x$.
• Distributing to only one term. $3(x + 4)$ is $3x + 12$, not $3x + 4$.

Sample problems

These problems come from the same generator as the worksheet above, three at each difficulty level. Press Generate for a fresh set.

Easy

1. $x + 10 = 25$
2. $8x = 32$
3. $7x = 63$

Medium

4. $8x + 7 = 63$
5. $3x + 9 = 27$
6. $7x + 4 = 67$

Hard

7. $4x + 5 = 1x + 23$
8. $2(x + 4) = 12$
9. $6x + 4 = 3x + 28$

Tips for teachers and parents

• A balance-scale picture helps younger students see why both sides must change together.
• Ask for one operation per line on Medium and Hard worksheets, written as "−3 both sides" or "÷5 both sides" in the margin.
• Checking by substitution is quick here because every answer is a small whole number.

Related topics

• Distributive Property Algebra
• Systems of Equations Algebra 2
• Quadratic Equations Algebra 2