Question
The teacher asks the students to give an equation. The equations are as follows
Robert: 2 times a number is 2 greater than the number
Bob: 3 times a number is 3 is greater than the number
Col: 4 added to a number is the same as 5 added to a number
Sam: 4 times a number is the same as 5 times a number
The student who gave an equation that has 0 as the solution is
- Robert
- Bob
- Col
- Sam
Hint:
An equation has a constant, variable and an equal to sign. It has two sides LHS and RHS. A linear equation in one variable is equation with only one variable and in which the highest degree is 1. Here, we have to find the value of unknown value, by operating both sides with the same number so that the equation will be balanced.
The correct answer is: Sam
In the question the teacher has given four different equations in word form.
We have find the student whose solution to the equation is 0.
Step 1: Convert word problem to numerical equation.
So, the equation for
Robert is 2x= 2+x ..................(1)
Bob is 3x=3+x ...................(2)
Col is 4+x= 5+x ....................(3)
Sam is 4x= 5x ...................(4)
In eq. 3 the unknown terms are same on both sides which on solving got cancelled. Thus, eq. 3 has no solution.
Bring all the terms containing variables in one side by operating same numbers on both sides to balance the equation.
Step 2: In eq.1 subtract both sides by x.
2x-x= 2+x-x
2x-x= 2
x= 2
So, the solution for eq. 1 is 2.
Step 3: In eq. 2 subtract each term by x.
3x-x= 3+x-x
3x-x= 3
2x= 3 ...................(5)
Step 4: In eq. 5 divide both sides by 2.
So, the solution for the equation 2 is 
.
Step 5: In equation 4 subtract both sides by 4x.
4x-4x= 5x-4x
0= 5x-4x
x=0
So, the solution for eq. 4 is 0.
therefore, the correct option is d, i.e., Sam.
A linear equation in one variable is equation with only one variable and in which the highest degree is 1. A linear equation has no solution if it has same terms on both sides of the equation. Like terms in an equation are the terms having same variable of same power in which the coefficient may not be the same whereas unlike terms are the terms which don't have same variable. Addition and subtraction are possible in like terms but not in unlike terms.
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A linear equation in one variable is equation with only one variable and in which the highest degree is 1. A linear equation in one variable can be solved by placing the unknown values on one side and known values on another side of the equation. it is important to operate equal terms on both sides so that the equation will remain balanced.
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A linear equation in one variable is equation with only one variable and in which the highest degree is 1. A linear equation in one variable can be solved by placing the unknown values on one side and known values on another side of the equation. it is important to operate equal terms on both sides so that the equation will remain balanced.
Number of solutions for 
is
Standard form of linear equation in one variable is ax+b=0. If x=
, then the solutions will be one. If both sides of the equation have same variable and constants then the equation has infinitely many solution.
Number of solutions for is
Standard form of linear equation in one variable is ax+b=0. If x=, then the solutions will be one. If both sides of the equation have same variable and constants then the equation has infinitely many solution.
