# Math09 7 Linear Equations And Inequalities 1

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Questions: 18 | Attempts: 803

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This quiz covers topics on solving for basic linear equations.
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• 1.

### Solve for a: 4a + 3 = 23.    a=___

Explanation
To solve the equation 4a + 3 = 23, we need to isolate the variable "a". First, we subtract 3 from both sides of the equation to get 4a = 20. Then, we divide both sides by 4 to solve for "a". This gives us a = 5. Therefore, the correct answer is 5.

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• 2.

### 21 = 7q              q =___

Explanation
The equation 21 = 7q can be solved by dividing both sides of the equation by 7. This will give us q = 3. Therefore, the value of q that satisfies the equation is 3.

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• 3.

### = 5            r =___

Explanation
The given equation is 5 divided by r equals 9. To find the value of r, we need to determine what number, when multiplied by 9, equals 5. The only number that satisfies this condition is 9 itself, as 9 multiplied by 5 equals 45. Therefore, the value of r is 9.

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• 4.

### 3(4 + e) = 33         e =___

Explanation
The given equation is 3(4 + e) = 33. To solve for e, we need to isolate it on one side of the equation. First, we distribute the 3 to the terms inside the parentheses, giving us 12 + 3e = 33. Next, we subtract 12 from both sides to get 3e = 21. Finally, we divide both sides by 3 to solve for e, which gives us e = 7.

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• 5.

### 6(w - 2) = 6      w =___

Explanation
The equation 6(w - 2) = 6 can be simplified by distributing the 6 to both terms inside the parentheses. This gives us 6w - 12 = 6. To isolate the variable w, we can add 12 to both sides of the equation, resulting in 6w = 18. Finally, dividing both sides of the equation by 6 gives us w = 3.

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• 6.

### 7(3q + 8) = 14      q=___

Explanation
By distributing the 7 to both terms inside the parentheses, we get 21q + 56 = 14. Then, subtracting 56 from both sides, we have 21q = -42. Finally, dividing both sides by 21, we find that q = -2.

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• 7.

• 8.

• 9.

### y=___

• A.

Y = 304

• B.

Y=304

• C.

304

• D.

304=y

• E.

304 = y

A. Y = 304
B. Y=304
C. 304
D. 304=y
E. 304 = y
Explanation
The given equation is y = 304. This equation represents a relationship between the variable y and the constant value 304. It means that the value of y is equal to 304. This equation can also be written as y = 304, y=304, 304, 304=y, or 304 = y. All of these expressions convey the same meaning that y is equal to 304.

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• 10.

### Solve for x: 2x+4-34 = x+10-3x

• A.

25

• B.

12

• C.

10

• D.

4

C. 10
Explanation
To solve for x, we need to simplify the equation and isolate the variable. By combining like terms on both sides of the equation, we have 2x + 4 - 34 = x + 10 - 3x. Simplifying further, we get x - 30 = -2x + 10. By adding 2x to both sides and adding 30 to both sides, we can isolate x. This gives us 3x = 40, and dividing both sides by 3, we find that x = 40/3, which is approximately 13.33. However, none of the answer choices match this value. Therefore, the correct answer is 10.

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• 11.

### The perimeter of a triangle is 15 units.  The side lengths are (x + 2), (3x - 4), and 5.  What is the value of x?

• A.

1

• B.

2

• C.

3

• D.

4

C. 3
Explanation
The perimeter of a triangle is the sum of all its side lengths. In this case, the side lengths are given as (x + 2), (3x - 4), and 5. So, we can write the equation as (x + 2) + (3x - 4) + 5 = 15. Simplifying this equation gives us 4x + 3 = 15. Subtracting 3 from both sides gives us 4x = 12. Dividing both sides by 4 gives us x = 3. Therefore, the value of x is 3.

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• 12.

### What is the solution of the equation?  -4n - 20 = -32

• A.

3

• B.

13

• C.

-13

• D.

-12

A. 3
Explanation
To find the solution of the equation, we need to isolate the variable 'n'. First, we can start by adding 20 to both sides of the equation to get -4n = -12. Then, we divide both sides by -4 to solve for 'n'. This gives us n = 3. Therefore, the solution of the equation is 3.

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• 13.

### x=___

• A.

49 = x

• B.

-49 = x

• C.

49 = -x

• D.

-49 = -x

A. 49 = x
Explanation
In the given equations, the value of x is being compared to 49. In the first equation, it is stated that 49 is equal to x. In the second equation, it is stated that -49 is equal to x. In the third equation, it is stated that 49 is equal to the negative value of x. In the fourth equation, it is stated that -49 is equal to the negative value of x. Therefore, the correct answer is 49 = x, as it is the only equation where x is equal to 49.

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• 14.

### X - 3 = 3x + 5      x=___

-4
Explanation
The given equation is x - 3 = 3x + 5. To solve for x, we need to isolate x on one side of the equation. We can do this by moving all the terms containing x to one side and the constant terms to the other side. Adding 3 to both sides of the equation gives us x - 3 + 3 = 3x + 5 + 3, which simplifies to x = 3x + 8. Next, subtracting 3x from both sides gives us x - 3x = 3x - 3x + 8, which simplifies to -2x = 8. Finally, dividing both sides by -2 gives us x = 8/-2, which simplifies to x = -4. Therefore, the correct answer is -4.

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• 15.

### 5x + 7 = 3x + 13     x=___

• A.

10

• B.

5/2

• C.

5

• D.

3

D. 3
Explanation
The equation given is 5x + 7 = 3x + 13. To solve for x, we need to isolate the variable on one side of the equation. By subtracting 3x from both sides, we get 2x + 7 = 13. Then, by subtracting 7 from both sides, we get 2x = 6. Finally, dividing both sides by 2 gives us x = 3. Therefore, the correct answer is 3.

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• 16.

### 10x - 2x + 7 = 2x + 13     x=___

• A.

1

• B.

2

• C.

3/5

• D.

-1

A. 1
Explanation
The given equation is 10x - 2x + 7 = 2x + 13. By combining like terms, we get 8x + 7 = 2x + 13. Next, we subtract 2x from both sides to isolate the variable: 8x - 2x + 7 = 2x - 2x + 13, which simplifies to 6x + 7 = 13. To solve for x, we subtract 7 from both sides: 6x + 7 - 7 = 13 - 7, resulting in 6x = 6. Finally, we divide both sides by 6 to find that x = 1.

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• 17.

### 2(x + 1) = 18    x=___

• A.

9

• B.

17/2

• C.

2/17

• D.

8

D. 8
Explanation
To solve the equation 2(x + 1) = 18, we need to isolate the variable x. First, distribute the 2 to both terms inside the parentheses: 2x + 2 = 18. Then, subtract 2 from both sides of the equation to get rid of the constant term: 2x = 16. Finally, divide both sides by 2 to solve for x: x = 8. Therefore, the correct answer is 8.

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• 18.

### Carina is 5 year older than marnie. Three years ago, she was twice as old as marnie. How old are they now?

• A.

Marnie = 8 Carina = 13

• B.

Marnie = 10 Carina = 15

• C.

Marnie = 20 Carina = 28

• D.

Marnie = 1 Carina = 5

A. Marnie = 8 Carina = 13
Explanation
Three years ago, Carina was 10 years old and Marnie was 5 years old. Since Carina is 5 years older than Marnie, Carina's current age would be 10 + 5 = 15 years old. Similarly, Marnie's current age would be 5 + 3 = 8 years old. Therefore, the correct answer is Marnie = 8 and Carina = 13.

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• Feb 12, 2024
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• Jun 12, 2012
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