Do you think you know algebra? Would you be willing to try this quiz? Algebra is the study of mathematical symbols and the rules for shaping these symbols. It represents a connection between itself and all types of mathematics. The more essential parts of algebra are called elementary algebra. The more advanced algebra is called abstract algebra or modern algebra. If you want to put your algebra skills to the test, stop right here and take this quiz.

Questions and Answers

- 1.
### Simplify the following (do not leave spaces in your answers) a) 6a + 7b + 3a + 9b = ________ b) 10a + 9b + a + 5b = ________ c) a + 8b + 7a + 2b = ________ d) a + 2b + 2 + 4a + 6b + 1 = ________ e) 10a + 9b + 2 + 4a + 7b + 5 = ________ f) 3a - 9b + 3 - 9a + 8b + 4 = ________ g) -10a + 10b + 3 + 3a + 5b + 1 = ________ h) 7a - 8b + 10 + 7a - 4b + 8 = ________ i) 8a - 2b + 2 + 7a - 10b + 4 = ________ j) 10a + 5b + 7 - 2a - 2b + 2 = ________

- 2.
### Multiply out: a) 4(7z - 10) = ________ b) 10(-9e - 5) = ________ c) 6(4f - 7) = ________ d) 9(-4g + 10) = ________ e) 2(7x - 4) = ________

Explanation

The given expressions are obtained by multiplying the number outside the parentheses with each term inside the parentheses using the distributive property. Therefore, the correct answers are obtained by multiplying 4 with (7z - 10), 10 with (-9e - 5), 6 with (4f - 7), 9 with (-4g + 10), and 2 with (7x - 4), respectively.Rate this question:

- 3.
### Multiply out and simplify the following: a) 2(9b + 4) + 4(8b + 6) = ________ b) 5(6y + 7) + 4(y + 3) = ________ c) 5(8k + 9) + 4(5k + 9) = ________ d) 2(3c + 1) + 5(6c + 9) = ________ e) 3(3v + 8) + 5(4v + 9) = ________

Explanation

The given expressions involve multiplying out and simplifying the given equations. In each case, we distribute the numbers outside the parentheses to the terms inside the parentheses, and then combine like terms. For example, in the first expression, 2(9b + 4) + 4(8b + 6), we multiply 2 by each term inside the first set of parentheses and 4 by each term inside the second set of parentheses. Then, we combine like terms to get 18b + 8 + 32b + 24, which simplifies to 50b + 32. Similarly, we follow the same steps for the other expressions to obtain their simplified forms.Rate this question:

- 4.
### Multiply out and simplify the following: a) 5(4m + 6) - 10(9m + 2) = ________ b) 3(6h + 3) - 10(5h + 7) = ________ c) 10(7e + 8) - 8(3e + 2) = ________ d) 4(2q + 8) - 9(7q + 8) = ________ e) 8(s + 6) - (4s + 5) = ________

Explanation

The given expressions are simplified by distributing the numbers outside the parentheses to the terms inside the parentheses and then combining like terms. For example, in the first expression, 5 is multiplied to both terms inside the parentheses (4m and 6), and 10 is multiplied to both terms inside the second parentheses (9m and 2). Then, the like terms are combined to get the simplified expression -70m + 10. The same process is followed for the rest of the expressions to obtain the given answers.Rate this question:

- 5.
### Work out the following: a) 10w + 9z when w = 9 and z = -6. ________ b) 6n - 8j when n = -2 and j = -2. ________ c) 5a + r when a = -1 and r = 10. ________ d) f - 8g when f = 10 and g = -6. ________ e) 4k + 7m when k = -8 and m = -3. ________

Explanation

a) The expression 10w + 9z can be evaluated by substituting w = 9 and z = -6. Thus, 10(9) + 9(-6) = 90 - 54 = 36.

b) Similarly, substituting n = -2 and j = -2 in the expression 6n - 8j gives us 6(-2) - 8(-2) = -12 + 16 = 4.

c) Substituting a = -1 and r = 10 in the expression 5a + r gives us 5(-1) + 10 = -5 + 10 = 5.

d) Substituting f = 10 and g = -6 in the expression f - 8g gives us 10 - 8(-6) = 10 + 48 = 58.

e) Finally, substituting k = -8 and m = -3 in the expression 4k + 7m gives us 4(-8) + 7(-3) = -32 - 21 = -53.Rate this question:

- 6.
### Solve the following: a) 9e - 9 = 3e - 15 e=________ b) 3v + 28 = 8v - 2 v = ________ c) 9b + 6 = 8b - 1 b = ________ d) 6p + 9 = 5p + 13 p = ________ e) 2n - 10 = 3n - 5 n = ________

- 7.
### Solve the following equation 5(2a+3) = 25 a = ________

Explanation

To solve the equation, we can start by distributing the 5 to the terms inside the parentheses: 5(2a+3) = 25 becomes 10a + 15 = 25. Next, we can isolate the variable by subtracting 15 from both sides of the equation: 10a = 10. Finally, we can solve for a by dividing both sides of the equation by 10: a = 1.Rate this question:

- 8.
### Solve the equation a=________

Explanation

The equation states that "a" is equal to the number that can replace the blank space in the equation. Since the equation only consists of the number 20, the value of "a" must be 20 in order for the equation to be true.Rate this question:

- 9.
### Solve the equation a=________

Explanation

The equation is asking for the value of 'a' that satisfies the equation. The correct answer is -2.4 or -12/5, which means that either of these values can be substituted for 'a' in the equation to make it true.Rate this question:

- 10.
### Solve the equation 2(3a - 5) - 5(2a + 3) = 15 a=________

Explanation

To solve the equation, we can start by distributing the numbers outside the parentheses. This gives us 6a - 10 - 10a - 15 = 15. Next, we can combine like terms by adding 6a and -10a to get -4a. This gives us -4a - 10 - 15 = 15. We can then combine the constants -10 and -15 to get -25. This gives us -4a - 25 = 15. To isolate the variable, we can add 25 to both sides of the equation, resulting in -4a = 40. Finally, we can divide both sides of the equation by -4 to solve for a, which gives us a = -10.Rate this question:

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