Algebra is a muscle—you have to train it. Use this drill set to build the speed and accuracy needed for exams.

The Routine: Solve the problems below. If you get one wrong, review the example, reset the drill, and try again until you hit 100% accuracy without thinking twice.

The Logic: Inverse operations. Undo the addition/subtraction first to isolate the variable term, then undo the multiplication/division.

Example: Solve $3x + 4 = 19$

• Subtract 4: $3x = 15$
• Divide by 3: $x = 5$

Drill:

Solve for $y$: $5y - 7 = 18$

Solve for $a$: $\frac{a}{4} + 2 = 9$

The Logic: The Distributive Property. Multiply the outside 'visitor' by every term inside the house. Then, group your families (like terms).

Example: Simplify $2(x + 4) - 3x$

• Expand: $2x + 8 - 3x$
• Combine: $(2x - 3x) + 8 = -x + 8$

Drill:

Simplify: $5m + 4(2m - 3)$

Simplify: $3(k + 2) - 6$

The Logic: Migration. Move all variables to the left and all numbers to the right (or vice versa) to balance the scale.

Example: Solve $5x - 2 = 2x + 10$

• Subtract $2x$: $3x - 2 = 10$
• Add 2: $3x = 12$
• Result: $x = 4$

Drill:

Solve for $p$: $7p + 4 = 3p - 12$