Balance both sides! Use inverse operations to solve one-step equations with confidence and connect algebra to everyday situations. ⚖️➗
Solve equations step-by-step using visual, numerical, and word-problem formats!
Identify the correct inverse operation!
Click all correct options
Solve equations and verify your answers!
Turn a story into an equation and solve it!
Arrange the steps for a multiplication equation!
Drag to sort or use ↑↓ buttons to adjust · Correct Order
Learn the balance strategy, connect to real-life contexts, and verify every solution!
Equations are balanced statements. One-step equations require just one operation to isolate the variable, making them perfect for building algebra confidence!
Math Sentence
An equation states two expressions are equal, like 3x + 4 = 10. The equals sign means both sides balance!
One-Step Focus
One-step equations include just one operation with the variable: x + 5 = 12 or 6x = 42. Easy to solve!
Goal
Our goal is to isolate the variable (get x alone). Use inverse operations to undo what's done to x!
Real Example
Money saved (s) plus $15 equals $47. Equation: s + 15 = 47. Solve s by subtracting 15!
Treat the equals sign like a balance scale. Whatever you do to one side, do to the other!
Adding or subtracting on only one side. Always mirror operations on both sides!
Budgeting, distance-rate-time problems, temperature conversions
Write 3 real-life stories, each with a simple equation to solve.
Inverse operations are the mathematical undo button. Use them to cancel the operation attached to the variable and isolate it!
Addition ↔ Subtraction
If equation adds 9, subtract 9 to undo it. x + 9 = 20 → x = 11. They cancel each other!
Multiplication ↔ Division
If equation multiplies by 4, divide by 4. 4x = 28 → x = 7. Inverses undo operations!
Undoing Order
Undo operations in reverse: subtract before dividing. Example: 2x + 5 = 19 → subtract 5, then divide by 2.
Balance Picture
Imagine removing equal weights from both sides of a scale. Inverses keep the scale balanced!
Draw arrows showing which operation you're undoing. This keeps steps clear!
Dividing when you should subtract, or vice versa. Identify the operation on the variable first!
Diet tracking (calories consumed vs. burned), financial planning
Make a two-column chart: operation vs. inverse. Fill it with examples.
For addition and subtraction equations, use the opposite operation to isolate the variable. Remember to maintain balance by applying the same step to both sides!
Addition
x + 14 = 29 → subtract 14 from both sides: x = 15
Subtraction
x - 7 = 18 → add 7 to both sides: x = 25
Negative Check
n - 10 = -4 → add 10 to both sides: n = 6. Works even with negative answers!
Word Problem
James spent $9 and has $15 left. Equation: s - 9 = 15 → s = 24. He started with $24!
Check by plugging the solution back into the equation. If both sides equal, you’re correct!
Subtracting when you should add. Read the equation aloud to clarify.
Budget adjustments, temperature changes, score tracking
Create 5 equations with answers between 1 & 50. Solve and check each.
Use division to undo multiplication and multiplication to undo division. Identify which operation is applied to the variable and reverse it!
Multiplication
6x = 54 → divide both sides by 6: x = 9
Division
x ÷ 8 = 6 → multiply both sides by 8: x = 48
Fractions
x/5 = 12 → multiply by 5: x = 60. Fractions mean division!
Real Context
Total price is $45 for 9 identical items. Equation: 9p = 45 → p = $5 each
Write division equations as fractions to recognize the multiplication inverse faster!
Dividing by the wrong number. Always divide by the coefficient (the number in front of the variable)!
Unit prices, recipe scaling, team grouping
Solve 3 equations that involve division written as fractions.
Checking solutions prevents careless mistakes. Substitute your answer back into the original equation and verify both sides match!
Substitute Back
After finding x, plug it back: If x = 7 works in 3x + 2 = 23, then 3(7) + 2 = 23. Balanced!
Left vs Right
Evaluate both sides. If left side equals right side, the solution is correct. If not, redo. ✍️
Catch Mistakes
If 5x = 30 and you got x = 4, plug it in: 5×4 = 20, not 30! Checking catches errors!
Word Problem
If 8 tickets cost $64, dividing gives $8 per ticket. Multiply to confirm: 8×8 = 64 ✔️
Always add the word 'Check' after solving. Habitual checking builds accuracy!
Skipping the check and carrying errors forward. One-minute checks save lots of time later!
Finance balancing, coding (debugging), engineering calculations
Solve 5 equations and show checks beside each solution.
One-step equations appear anywhere numbers change by consistent amounts. Recognizing and solving them makes everyday decision-making smarter!
Budgeting
Total savings s plus $20 = $95. Solve s + 20 = 95 to find starting savings. Budget planning uses equations!
Cooking
Recipe needs ingredients per serving. If one tray holds 8 cookies and you baked 64, equation 8t = 64 finds trays!
Sports
Team scored t touchdowns worth 7 points each plus 2 field goals. Total 34 points: 7t + 6 = 34. Algebra in action!
Technology
Video game XP uses formulas like XP = 500 + 120l. Plug in level l to find experience points needed!
Whenever you see 'each,' 'per,' or 'plus a fee,' consider writing an equation!
Estimating instead of calculating. Equations give exact answers—use them!
Shopping deals, construction measurements, fitness plans
Write one equation for each family member’s daily routine. Solve them together!