ASVAB CampLinear Equations flashcards
8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.
Rule · 1/8
What is the balance rule for solving an equation?
Do the same thing to both sides: add, subtract, multiply or divide both sides by the same number. Never multiply both sides by zero (that wipes out the solution, leaving 0 = 0), and never divide by zero, which is undefined.
Strategy · 2/8
In what order do you solve a two-step equation such as 5x + 3 = 38?
Undo the operations in reverse order using inverse operations: subtract 3 first to get 5x = 35, then divide by 5 to get x = 7. Check: 5(7) + 3 = 38.
Common trap · 3/8
Solving −4x = 28: what is the common mistake?
Dropping the negative sign. Divide both sides by −4, sign included: x = −7. Writing x = 7 gives the opposite of the correct answer. Check: −4(−7) = 28.
Strategy · 4/8
How do you solve with x on both sides, e.g. 9x − 2 = 4x + 18?
Subtract the smaller x term from both sides to keep a positive coefficient: subtract 4x to get 5x − 2 = 18, add 2 to get 5x = 20, so x = 4.
Rule · 5/8
How do you clear fractions or decimals from an equation?
Multiply every term on both sides by the LCD (or a power of ten for decimals), constants included. For , multiply by 12: 4x + 3x = 84, so x = 12.
Fact · 6/8
What does it mean if the variable cancels out completely?
A false leftover such as 5 = 9 means the equation is a contradiction with no solution. A true leftover such as 3 = 3 means it is an identity: every real number is a solution.
Strategy · 7/8
Translate: four less than twice a number is 18.
'Is' means equals and 'less than' subtracts in reverse order: 2n − 4 = 18. Then 2n = 22 and n = 11.
Formula · 8/8
How do you solve the formula P = 2l + 2w for l?
Treat the other letters as numbers and use inverse operations: subtract 2w, then divide by 2, giving .