Olympiad Test: Simple Equations - Class 7 MCQ

Solution:

• To express "p multiplied by 16", we write it as 16p.
• This indicates that p is being multiplied by 16.

The correct expression is therefore 16p.

Number is x. When two is subtracted from it, we write this as x - 2. This expression equals 8. Therefore, the equation is:

x - 2 = 8.

Seven times a number plus 7 gets you 77 can be expressed as an equation:

• The equation is 7x + 7 = 77.

To break this down:

• 7x represents seven times a number.
• Adding 7 to that gives us the total.
• Setting this equal to 77 completes the equation.

One third of a number is represented as (1/3)x.

When you add 3 to this, it becomes:

• (1/3)x + 3

This sum equals 30, leading to the equation:

• (1/3)x + 3 = 30

To isolate x, subtract 3 from both sides:

• (1/3)x = 30 - 3
• (1/3)x = 27

Next, multiply both sides by 3 to solve for x:

• x = 27 × 3
• x = 81

Thus, the equation (1/3)x + 3 = 30 is correctly formed.

Solution:

To solve the equation p + 4 = 15, follow these steps:

• Start with the equation: p + 4 = 15
• Subtract 4 from both sides:
• p = 15 - 4
• Calculate the right side:
• p = 11

The solution is p = 11.

X-7 = 3
X = 3+7
ans. Is x = 10

Solution:

To solve the equation, we can break it down step by step:

• Let m be the variable we are solving for.
• The equation states that two times m equals seven.
• To isolate m, we divide both sides of the equation by 2.

This gives us:

• m = 7 / 2

Thus, the solution to the equation is:

• m = 3.5

Solution:

To solve the equation 3m/5 = 6, follow these steps:

• First, multiply both sides by 5 to eliminate the fraction:
• 3m = 6 * 5
• This simplifies to 3m = 30.

Next, divide both sides by 3:

• m = 30 / 3
• This gives m = 10.

Thus, the solution to the equation is m = 10.

Solution:

To solve the equation (a/2) + 2 = 8, follow these steps:

• Start with the equation: (a/2) + 2 = 8
• Subtract 2 from both sides to isolate the term with a:
• a/2 = 6
• Multiply both sides by 2 to solve for a:
• a = 12

The solution to the equation is a = 12.

Solution:

To solve the equation, follow these steps:

• Start with the equation: 2a - 2 = 20.
• Add 2 to both sides to isolate the term with a:
• 2a = 20 + 2
• This simplifies to 2a = 22.
• Now, divide both sides by 2:
• a = 22 / 2
• This results in a = 11.

Thus, the value of a is 11.

Solution:

To solve the equation 4m - 2 = 18, follow these steps:

• Start with the equation: 4m - 2 = 18.
• Add 2 to both sides to isolate the term with m:
• 4m = 18 + 2
• 4m = 20
• Next, divide both sides by 4 to solve for m:
• m = 20 / 4
• m = 5

The solution is m = 5.

The sum of three times a number and 11 is 32. Find the number.

Let the unknown number be x. The equation can be set up as follows:

• Three times the number: 3x
• The equation: 3x + 11 = 32

To solve for x, follow these steps:

• Subtract 11 from both sides:
• 3x = 32 - 11
• 3x = 21
• Now, divide both sides by 3:
• x = 21 / 3
• x = 7

The required number is 7. You can check this by calculating:

• 3 times 7 + 11 = 21 + 11 = 32

Solution:

To solve the equation 2p - 1 = 23, follow these steps:

• First, add 1 to both sides:
• 2p - 1 + 1 = 23 + 1
• This simplifies to 2p = 24.
• Next, divide both sides by 2:
• 2p / 2 = 24 / 2
• This gives us p = 12.

To verify, substitute p = 12 back into the original equation:

• Left-hand side: 2p - 1 = 2 × 12 - 1 = 24 - 1 = 23
• Right-hand side: 23

Since both sides are equal, the solution is confirmed as p = 12.

To solve the equation:

• Start with the equation: 3a/10 = 6.
• Multiply both sides by 10 to eliminate the fraction:
• 3a = 10 * 6
• 3a = 60
• Now, divide both sides by 3:
• a = 60 / 3
• a = 20

The solution is a = 20.

To solve the equation 3z – 2 = 46:

• First, add 2 to both sides to isolate the term with z:
• 3z – 2 + 2 = 46 + 2
• This simplifies to 3z = 48.
• Next, divide both sides by 3 to solve for z:
• 3z / 3 = 48 / 3
• This gives z = 16.

The solution to the equation is z = 16.

The solution of the equation 5x + 7 = 17 is x =

To solve the equation, follow these steps:

• Start with the equation: 5x + 7 = 17.
• Subtract 7 from both sides to isolate the term with x:
  • 5x + 7 - 7 = 17 - 7
  • This simplifies to: 5x = 10.
• Next, divide both sides by 5 to solve for x:
  • 5x / 5 = 10 / 5
  • This gives: x = 2.

To verify the solution, substitute x back into the original equation:

• 5(2) + 7 = 10 + 7 = 17, which matches the right-hand side.

Thus, the solution is confirmed as correct: x = 2.

Three times a number plus 11 equals 32.

To find the number, follow these steps:

• Let the unknown number be x.
• The equation can be written as: 3x + 11 = 32.
• Subtract 11 from both sides to isolate 3x: 3x = 32 - 11.
• This simplifies to: 3x = 21.
• Now, divide both sides by 3: x = 21 / 3.
• Thus, x = 7.

The required number is 7. You can verify this by calculating 3 times 7 plus 11, which equals 32.