FutureStepsA quick starting check.
- Use addition and subtraction with positive and negative numbers.
- Understand multiplication and division as inverse operations.
- Know that a variable represents a number.
Build the method, one step at a time.
Keep both sides balanced
In , the expression on the left must have the same value as the number on the right. Subtracting 4 from both sides keeps the equation equivalent. Subtracting 4 from only one side changes the statement.
Adding or subtracting the same amount on both sides preserves equality. Multiplying or dividing both sides by the same nonzero number also preserves equality. Write the operation on both sides so that each change has a reason.
Undo the outside operation first
To build from x, you multiply by 3 and then add 4. A convenient way to solve is to reverse that order: first subtract 4, then divide by 3. The goal is to leave x by itself.
For , first undo subtracting 2 by adding 2. Then undo dividing by 4 by multiplying by 4. You do not always divide in the second step; choose the inverse of the operation actually attached to the variable.
A substitution check catches sign mistakes
Put your answer into the original equation, not just the last simplified line. If you think x is 7 in , evaluate . It equals 25, so the original equality holds.
This check is especially helpful when the coefficient is negative. A negative coefficient does not force a negative answer. The sign of the solution depends on the whole equation, so calculate and verify rather than guessing from one symbol.
Two worked examples.
Solve 3x +
- Subtract 4 from both sides: , so .
- Divide both sides by 3: .
- Substitute 7 into the original equation: .
Check your reasoning: The original left and right sides both equal 25. Seven satisfies both operations, not just the multiplication.
Solve -2x +
- Subtract 5 from both sides to get .
- Divide both sides by -2, not by 2: .
- Check the original left side: .
Check your reasoning: A negative times a negative is positive. Substituting positive 4 instead would give -3, so the sign matters.
Try it before you reveal it.
Write down your thinking. Open a hint if you get stuck, then compare your method with the explanation.
Practice 1
Solve .
Show a hint
Undo subtracting 7 before undoing multiplication by 4.
Show the answer and explanation
Add 7 to both sides to get , then divide by 4. Check: .
Practice 2
Solve .
Show a hint
After you add 2, choose the inverse of division by 4.
Show the answer and explanation
Add 2 to get . Multiply both sides by 4 to get . Check: .
Practice 3
A club charges a 6-dollar setup fee and 3 dollars for each badge. The total is 24 dollars. How many badges were ordered?
Show a hint
Let b represent the number of badges. Write 3b + .
Show the answer and explanation
6 badges
Subtract the setup fee: . Divide by 3: . The check includes the fee: six badges cost 18 dollars, and 18 dollars plus 6 dollars is 24 dollars.
What to take with you.
Name the operation you are undoing, apply it to both sides, and use the original equation to check your answer.
Try explaining one example without looking at the steps. If a step is hard to explain, revisit that part before moving on.
Give me a two-step equation and ask which operation I would undo first. Check one step at a time, then ask me to verify my answer in the original equation.
Eligible students ages 13 and older with Study access can sign in and use this prompt for more practice. Check AI explanations against your class materials.
Continue in StudyWritten by FutureSteps for study and review. This lesson expands a topic in our Texas starter collection. Course reference: Texas TEKS · Grade 7 Mathematics (§111.27(b)(11)(A); §111.27(b)(11)(B)). These references do not imply endorsement, complete standard coverage or assessed mastery. Follow your school’s materials and course sequence.
Explore more in the 7th grade learning guide.