Test: Linear Equations- 2 - Grade 9 MCQ

To solve the equation 4y = 20, follow these steps:

• Divide both sides by 4:

y = 20 ÷ 4

• This simplifies to y = 5.

Thus, the solution is correct and complete.

Starting with the equation:

3x = 2x + 18

To solve for x, follow these steps:

• Subtract 2x from both sides:

3x - 2x = 18

• Simplify the left side:

x = 18

x = 4/5*(x + 10)

=> x = 4x/5 + 8

=> x - 4x/5 = 8

=> (5x - 4x)/5 = 8

=> x = 8 * 5 = 40

Verification / Checking-

LHS = x = 40

RHS = 4/5*(x + 10) = 4/5*(40 + 10) = 4/5 * 50 = 40

Given,

Sum of multiples of 7 = 357

Let the numbers be x, x + 7 , x + 14

ATP,

x + x + 7 + x + 14 = 357

3x + 21 = 357

3x = 357 - 21

3x = 336

x = 336/3

x = 112

Therefore,

the smallest multiple is x = 112 

To solve the equation, follow these steps:

1. Add 2 to both sides of the equation:

• x - 2 + 2 = 7 + 2

2. Simplifying gives:

• x = 9

To solve the equation 5t - 3 = 3t - 5:

1. Subtract 3t from both sides:
   • 5t - 3t - 3 = -5
   • Simplifying, we get: 2t - 3 = -5
2. Add 3 to both sides:
   • 2t - 3 + 3 = -5 + 3
   • Simplifying, we get: 2t = -2
3. Divide both sides by 2:
   • t = -2/2 = -1

Thus, the solution is t = -1.

To solve the equation 5x + 9 = 5 + 3x, follow these steps:

• Step 1: Subtract 3x from both sides:
• 5x - 3x + 9 = 5
• Simplifies to: 2x + 9 = 5
• Step 2: Subtract 9 from both sides:
• 2x = 5 - 9
• 2x = -4
• Step 3: Divide both sides by 2:
• x = -2

To solve the equation y + 3 = 10:

• Subtract 3 from both sides:
• y + 3 - 3 = 10 - 3
• Simplify:
• y = 7

Let the number be x.
So, the other number is (x + 15).
(x + 15) + x = 95
2x + 15 = 95
2x = 95 - 15
2x = 80
x = 40
So, the numbers are 40 and 55.

In an equation, the equality sign (=) indicates that the values of the expressions on both sides are equal. Therefore:

• The value of the expression on one side is equal to the value of the expression on the other side.

To solve the equation, we start with:

(2x/3) 1 = (7x/15) 3

First, we can eliminate the fractions by multiplying both sides by 15:

• Multiply the left side: 15 * (2x/3) = 10x
• Multiply the right side: 15 * (7x/15) = 7x

This gives us:

10x + 15 = 7x + 45

Next, we simplify the equation:

• Subtract 7x from both sides: 10x - 7x + 15 = 45
• This simplifies to: 3x + 15 = 45

Now, we isolate x:

• Subtract 15 from both sides: 3x = 30
• Finally, divide by 3: x = 10

The solution is:

x = 10

Subtract 5 from both sides to get 3x = 15. Dividing both sides by 3 gives x = 5.