Algebra: keep both sides balanced.
An equation says that two expressions have the same value. Solving an equation means finding a value that makes that statement true.
Reviewed · Official ASVAB scope and calculator guidance. Examples are original AptiStep material.
Use the same operation on both sides
For x + 7 = 19, subtract 7 from both sides. This keeps the equality true and leaves x = 12. “Moving a number across the equals sign” is a shortcut for that balanced operation. Remembering the operation is more reliable than memorizing a sign-changing trick.
Treat negative signs as part of the term
In 4y − 7 = 17, undo subtracting 7 by adding 7 to both sides: 4y = 24. Then y = 6. Substitution gives 24 − 7 = 17. If your result fails that check, return to the first line where the two sides stopped matching.
Distribute to every term inside parentheses
In 2(x + 3) = 14, the left side can be expanded to 2x + 6. Alternatively, divide both sides of the original equation by 2 to get x + 3 = 7. Either route gives x = 4. Multiplying only the x and leaving the 3 unchanged would change the expression.
Try a fresh equation
Solve 5z − 8 = 27.
Show the solution
Add 8: 5z = 35. Divide by 5: z = 7. Check the original equation: 5(7) − 8 = 35 − 8 = 27.
During review, identify the exact operation that went wrong. “I forgot to add 8 to both sides” gives you a specific habit to practice; “I am bad at algebra” does not.
Four fresh questions
Try each example before opening its answer. Then explain the step you used in your own words.
Solve 5x + 4 = 29.
Show answer and reasoning
x = 5
Subtract 4 from both sides: 5x = 25. Divide by 5: x = 5. Check in the original equation: 5(5) + 4 = 29.
Solve 3(y − 2) = 18.
Show answer and reasoning
y = 8
Divide both sides by 3: y − 2 = 6. Add 2 to both sides: y = 8. Check: 3(8 − 2) = 18.
Solve x/4 + 3 = 8.
Show answer and reasoning
x = 20
Subtract 3: x/4 = 5. Multiply both sides by 4: x = 20. Undo the addition before undoing the division.
Solve 2a + 5 = a + 12.
Show answer and reasoning
a = 7
Subtract a from both sides to obtain a + 5 = 12. Subtract 5: a = 7. Both original sides then equal 19.
Can you explain the method without looking?
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