1st term math RExam

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Questions and Answers

Which equation represents this sentence? Four times the sum of a number x and a number y is equal to 20.

4x + y = 20

4xy = 20

4 + x + y = 20

4(x + y) = 20 (correct)

Solve x – 5 = 21. What is x?

Solve 21 = 3p – 6. What is p?

9 (correct)

Solve 5 = 10 for x. Assume that a ≠ 0. Find x in 15 + ax.

x = −13/a Signup and view all the answers

Solve 4x – 5 = 41. What is x?

11.5 Signup and view all the answers

Solve 4(x + 9) = 6x – 4. What is x?

16 Signup and view all the answers

Solve 3 |y + 6| = 30. What are the possible values of y?

{–12, 8} Signup and view all the answers

Solve x + 15 = 2. 10 5. What is x?

–13 Signup and view all the answers

Solve x = 21/144. What is x?

0.1458 Signup and view all the answers

Solve 2x + 12/5 = 4y for x. What is x?

x = 10y − 12 Signup and view all the answers

Which equation represents this sentence? The sum of 5 times a number m and 12 is equal to 27.

5m + 12 = 27 Signup and view all the answers

Solve n − 8 = 5 and identify the property of equality used. What are the results?

–13; Subtraction Property of Equality Signup and view all the answers

Solve z + 12 = –3. What is z?

–15 Signup and view all the answers

Solve 1t = 10. 5. What is t?

5 Signup and view all the answers

If 3x – 6 = 42, what is the value of x?

12 Signup and view all the answers

Solve 8 = 11 – 3y. What is y?

1 Signup and view all the answers

Solve 5 – kx = 9 for x. Assume that k ≠ 0. What is x?

x = −4/k Signup and view all the answers

Solve 3x + 1 = 4x – 8. What is x?

9 Signup and view all the answers

Solve 5(2y + 1) = 4y + 10. What is y?

3/2 Signup and view all the answers

Solve 12/b = 10/15. What is b?

18 Signup and view all the answers

Solve 3/(x+4) = (x − 2)/4. What is x?

4 Signup and view all the answers

Which equation represents this sentence? The sum of five times a number and seven is equal to twelve.

5n + 7 = 12 Signup and view all the answers

Solve 1/a = 12/2. What is a?

6 Signup and view all the answers

Solve p + 8 = 15. What is p?

7 Signup and view all the answers

Solve bx − 4 = 5 for x. Assume that b ≠ 0. What is x?

x = 1/b Signup and view all the answers

Solve 3y + 6 = 18. What is y?

4 Signup and view all the answers

Solve 4m + 5 = 2m + 45. What is m?

20 Signup and view all the answers

Solve 5(r + 3) = 3r + 35. What is r?

4 Signup and view all the answers

Study Notes

Solving Equations

Solving for a variable: To solve an equation, isolate the variable on one side of the equation by performing the same operation on both sides.
Using properties of equality:
- Addition Property of Equality: Adding the same number to both sides of an equation does not change the solution.
- Subtraction Property of Equality: Subtracting the same number from both sides of an equation does not change the solution.
- Multiplication Property of Equality: Multiplying both sides of an equation by the same nonzero number does not change the solution.
- Division Property of Equality: Dividing both sides of an equation by the same nonzero number does not change the solution.
Solving multi-step equations: Combine like terms, use the properties of equality, and simplify to isolate the variable.
Solving equations with absolute values:
- Remember absolute value represents distance from zero.
- Solve two separate equations, one with the expression inside the absolute value being positive and the other being negative.

Writing Equations from Sentences

Identify the unknown: Determine the variable that represents the unknown quantity.
Translate words into symbols: Use mathematical symbols (+, -, ×, ÷, =) to represent the relationships described in the sentence.
Combine expressions: Combine the expressions according to the relationship expressed in the sentence.
Write the equation: Use the given information to write the equation in a standard mathematical format.