Simple Linear Equations Test - 4

Let the number be x

Substraction of 1/2 from x = x-1/2

Then multiplication of the result obtained by 1/2 =( x-1/2)1/2

Result got at last = 1/8

Then find the number?????

(x - 1/2) 1/2 =1/8

x - 1/2 =1/8 ×2

x-1/2 = 1/4

Do fraction of x - 1/2

2x-1/2 =1/4

Criss cross method

LHS goes to RHS and RHS goes to LHS

4(2x -1) = 2

8x - 4 = 2

8x = 2+4

8x = 6

Then

x = 6/8

x = 3/4

The point of Algebra is to isolate the variable so that we have  x alone on one side of the equation, and other numbers on the other.

Now, the first thing is to bring the  2x  over so that all of the numbers with  x  in them are on one side.

So, how do we do that? Well, if  2x is being added to  20,  then we can take away the  2x.  Why? Because addition is the opposite of subtraction. If I give the 20 a  2x, the reverse is to take it away.

I also have to do this to the other side. Think of it like a scale. I have to take the same weights away from both sides, or it gets unbalanced. To simplify  4x − 2x, I can just say  2x. Why? Because  4x = x + x + x + x, and  2x = x + x. As previously established, those two will cancel out two other  x 's, leaving  20=2x. 

Lastly, I want to divide by two so that I get the  x  alone. Multiplication is the opposite of division in the same way that addition is the opposite of subtraction.

So, the final answer is that  x = 10.

Let b be the base and a be the lengthbif side and p perimeter of the isoscles triangle itis given that b = 4/3 cm and p= 4 2/15 cm = 62/15 cm

but p = b +a+a ie

62/15 = 4/3 + 2a or 2a 62/15- 4/3 =( 62 -20)/15= 42/15= 14/5 ie a =7/5 cm

Let's consider that number to be 'x'..

So, twice the number (2x) is 12 greater than than the half of the number.

So the equation will be like,

2x=12+x/2

Solving this further,

2x=(24+x)/2

=> 4x=24+x

=>4x-x=24

=>3x=24

=>x=8..

So the number is "8".

Let the number be x

Twice it - 2x

Decrease 22- 2x - 22

According to this

2x - 22 = 48

2x = 20

x = 35

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be x/x + 8.

According to the given cndition,

x + 17/x + 8 – 1 = 3/2

= x + 17/x + 7 = 3/2

= 2(x + 17) = 3(x + 7)

= 2x + 34 = 3x + 21

= 34 − 21 = 3x − 2x

= x=13

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number = 13/21

Multiplying and dividing $\frac{2}{5}$ by 3

= $\frac{2}{5}\times \frac{3}{3}=\frac{6}{15}$

Comparing $\frac{6}{15}$ with $\frac{x}{15}$

we get, x = 6

Let the length of the pool be denoted by  l , and the breadth be denoted by  b

Then, the statement, “Its length is 2 m more than twice its breadth” is equivalent to writing:

l = 2b + 2 

Now, for a rectangle, the perimeter,  P,  is given by:

P = 2l + 2b

Substituting our expression for  l  gives:   

P = 2(2b + 2) + 2b = 6b + 4 = 154

which we can re-arrange to find:

6b = 150 ⟹ b = 25 

And plugging this into our expression for  l  yields:

l = 2b + 2 = 2 × 25 + 2 = 52 

Thus its length is 52m and its breadth is 25m

Let the three consecutive odd integers be x,x+2,x+4.

Then according to the problem,

x + x + 2 + x + 3 = 51

or, 3x + 6 = 51

or, 3x = 45

or, x = 15.

So the numbers are 15,17,19.

Let x be the age of Ramu. 5 times Ramu's age is 5x years. Now, Ramu's father is 5 years older than 5 times his son's (Ramu's) age. Therefore,

Age of Ramu's father = 5x + 5………………………………….……………..(1)

But by hypothesis, age of Ramu's father = 40 years…………………(2)

Equating equations (1) and (2),

5x + 5 = 40

Dividing throughout by 5,

x + 1 = 8 Subtracting 1 from both sides,

x + 1 - 1 = 8–1

Or, x = 7

Therefore, age of Ramu = 7 years (Proved)

v, a number. 36 less than 10 times the number. 

7x = 10x - 36

10x - 7x = 36

3x = 36

x = $\frac{36}{3}=12$

Given line is \(a x+b y+c=0\)

\(\Rightarrow b y=-a x-c\)

\(\Rightarrow y=\frac{-a}{b} x+\frac{-c}{b}\) is in the form of \(y=m x+c\)

where slope \(=m=\frac{-a}{b}\)

You can find any thing like this (the sum of x consecutive numbers, even numbers, multiples of 3 …) with a simple trick. If x is the first number, we know the next multiple of 8 is x + 8, and the one after that is x + 16. So that leaves us with

x + x + 8 + x + 16 = 888 . Combine like terms:

3x + 24 = 888. Subtract 24

3x = 864. Divide by 3

x = 288. The multiples are 288, 296, and 304

Now we are give that that 1/5 of one part is equal to 1/7 of the other. Hence the one part is 15 and another part is 21. Dividing 36 into two parts in such a way that 1/5 of one part is equal to 1/7of the other.

Let the measure of the supplementary angles be x and (x + 36). Therefore, measures of the supplementary angles are 72° and (72 + 36) i.e. 108°

Let the number of boys be 7x and that of girls be 5x.

According to the given condition, we have

Number of boys = Number of girls + 8

⇒ 7x = 5x + 8

⇒ 7x - 5x = 8 ..... [Transposing 5x to LHS]

⇒ 2x = 8

⇒ x =$\frac{8}{2}=4$

Therefore, number of boys = 7 × 4 = 28 and number of girls = 5 × 4 = 20

So, total number of children in the class =28+20=48.

Hence, the class strength is 48.