The 7-Day Algebra Reset

Remember: adding a negative moves left on a number line. Subtracting a negative removes a leftward move, so it becomes addition.

1. −7 + 12 =
2. 5 − (−9) =
3. −4 − 8 =

Explain aloud: Why is question 2 greater than 5?

Remember: grouping first, powers next, multiplication and division left to right, then addition and subtraction left to right.

4. 3 + 4 × 5 =
5. 18 ÷ 3 × 2 =
6. 2(7 − 3) + 5 =

Circle the operation you performed first in each expression.

Remember: a(b + c) = ab + ac. The outside factor belongs to every term in the group.

7. 3(x + 4) =
8. −2(5x − 3) =
9. 4(2y + 1) − 3 =

Put a small arrow from the outside factor to every term it multiplies.

Remember: x-terms combine with x-terms. Constants combine with constants. A term with x² does not combine with x.

10. 5x + 2x − 3 =
11. 4y + 6 − y + 2 =
12. 3a² + 2a − a² + 5a =

Underline each family of like terms with the same mark.

Remember: use the inverse operation and perform it on both sides. Then substitute your answer to check.

13. x + 7 = 19
14. −4x = 28
15. x ÷ 5 = −3

Write the checking substitution beside each answer.

Remember: in ax + b = c, undo b before dividing by a. Keep both sides balanced at every step.

16. 3x + 4 = 19
17. −2x − 5 = 11
18. 7x + 9 = −12

Name the inverse operation before writing it.

Remember: in y = mx + b, m is the change in y for each one-unit change in x, and b is the y-intercept.

19. For y = 2x + 1, find y when x = 3.
20. A line passes through (1, 4) and (5, 12). Find its slope.
21. Write a line with slope −3 and y-intercept 5 in slope-intercept form.

Complete the sentence: “A slope of ___ means y changes by ___ when x increases by 1.”