Algebra Quiz: Test Your Skills!

1. 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. _____

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.

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.

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

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.

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.

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3. Solve the following equation 5(2a+3) = 25 a = _____

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.

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.

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4. Solve the equation $\frac {2a+5} {3}=15$ a=_____

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.

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.

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5. 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) = _____

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.

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.

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6. 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 = _____

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Explanation

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7. 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) = _____

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.

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.

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9. Solve the equation $\frac {4(5a-3)} {3}=-20$ a=_____

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.

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.

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

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.

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.

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