Equations With One Variable - SAT Math

1. Identify the inverse operation to solve $x - 5 = 10$.

   Addition. Add 5 to both sides to isolate x.

2. What is the solution to $2x + 3 = 7$?

   $x = 2$. Subtract 3, then divide by 2.

3. Solve for $x$: $5 - x = 3$.

   $x = 2$. Subtract 5 from both sides, then multiply by -1.

4. Solve for $x$ if $x + 8 = 15$.

   $x = 7$. Subtract 8 from both sides.

5. What is the value of $x$ if $x + 9 = 15$?

   $x = 6$. Subtract 9 from both sides to isolate $x$.

6. Identify the value of $x$ in the equation $3x - 4 = 2$.

   $x = 2$. Add 4 to both sides, then divide by 3.

7. What is the solution to the equation $x + 5 = 12$?

   $x = 7$. Subtract 5 from both sides to isolate x.

8. What is the solution to the equation $2x + 5 = 11$?

   $x = 3$. Subtract 5 from both sides, then divide by 2.

9. Find the solution for $4x = 20$.

   $x = 5$. Divide both sides by 4 to isolate $x$.

10. Find the value of $x$ in $x/3 = 9$.

    $x = 27$. Multiply both sides by 3.

11. State the formula for solving the equation $ax + b = 0$.

    $x = -\frac{b}{a}$. Subtract $b$ from both sides, then divide by $a$.

12. What is the inverse operation for addition in an equation?

    Subtraction. Addition and subtraction are inverse operations.

13. Solve for $x$ in the equation $5x = 20$.

    $x = 4$. Divide both sides by 5.

14. What is the first step to solve $3(x - 2) = 12$?

    Distribute to get $3x - 6 = 12$. Apply the distributive property to remove parentheses.

15. What is the solution to the equation $2x + 3 = 11$?

    $x = 4$. Subtract 3 from both sides, then divide by 2.

16. What is the multiplicative identity property?

    For any number $a$, $a \times 1 = a$. Multiplying by 1 leaves any number unchanged.

17. State the commutative property of addition.

    $a + b = b + a$. Order of addends doesn't affect the sum.

18. What is the additive inverse property?

    For any number $a$, $a + (-a) = 0$. Any number plus its opposite equals zero.

19. What is the result of solving $x - 5 = -3$?

    $x = 2$. Add 5 to both sides.

20. Solve for $x$ in the equation $10 = 3x + 1$.

    $x = 3$. Subtract 1, then divide by 3.

21. What value of $x$ satisfies $x/4 = 3$?

    $x = 12$. Multiply both sides by 4 to isolate $x$.

22. What is the associative property of multiplication?

    $(ab)c = a(bc)$. Grouping factors doesn't change the product.

23. State the inverse operation for multiplication in an equation.

    Division. Multiplication and division are inverse operations.

24. State the property used to solve $x/3 = 4$.

    Multiplication. Multiply both sides by 3 to eliminate the fraction.

25. What is a linear equation?

    An equation of the form $ax + b = 0$. One variable raised to the first power.

26. What is the solution to $5 - 2x = 1$?

    $x = 2$. Subtract 5 from both sides, then divide by -2.

27. Find $x$ in the equation $6 = x + 2$.

    $x = 4$. Subtract 2 from both sides.

28. What operation is used to isolate a variable?

    Use inverse operations. Apply the opposite operation to both sides.

29. Solve the equation $7 - x = 4$.

    $x = 3$. Subtract 7 from both sides, then multiply by -1.

30. What is the definition of an equation?

    A statement that two expressions are equal. Shows two expressions have the same value.

31. Identify the solution for $3x - 4 = 2$.

    $x = 2$. Add 4, then divide by 3.

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