Question
Number of solutions for 
is
- One solution
- No solution
- Infinity many solution
- Cannot be determined
Hint:
An equation contains constants, variables and an equal sign. It has two sides called LHS and RHS. A linear equation in one variable is an equation with only one variable and the highest power of the variable should be one. Here, we have to find the number of solutions of the given linear equation in one variable which can be done by writing the given equation in standard form and comparing the it with the standard equation.
The correct answer is: One solution
The given equation is
Here, we have to find the number of solutions for the given equation.
Step 1: Solve the bracket.
Since, the variables and constants in both sides are different, so this equation don't have infinitely many solutions.
Bring all the terms containing variables in one side by operating same numbers on both sides to balance the equation.
Step 2: Multiply 10 on both sides.(LCM of 2 and 5 is 10.)
Step 3: Solve the brackets on both sides.
25x-125= -4x+16
Step 4: Add 4x on both sides.
25x-125+4x= -4x+16+4x
25x-125+4x= 16
Step 5: Add 125 on both sides.
25x-125+4x+125= 16+125
25x+4x= 16+125
Step 6: Solve both sides.
29x= 141 ...........(1)
Step 7: Write the eq. 1 in standard form,i.e., ax+b=0
29x-141=0 ...............(2)
Step 8: Compare eq. 2 with the standard equation.
On comparing eq. 2 with the standard equation we have, a= 29 and b= -141.
Since, x= 
So, the equation has only one solution.
therefore, the correct option is a,i.e., one solution.
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.
Related Questions to study
In a Halloween, if each house visited gives you 5 chocolates, initially you started with 10 chocolates by the end you have 150 chocolates, then the number of houses visited are
Like terms 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.
In a Halloween, if each house visited gives you 5 chocolates, initially you started with 10 chocolates by the end you have 150 chocolates, then the number of houses visited are
Like terms 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.
If five being added to twice a number and two being added to five times a number is same, then the number is
Like terms 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.
If five being added to twice a number and two being added to five times a number is same, then the number is
Like terms 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.
Mary bought some apples from the store, she gave half of the apples she bought to Adam, the 5 from the remaining to his brother. The apples she left with are 3. The number of apples she gave to Adam are
Like terms 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.
Mary bought some apples from the store, she gave half of the apples she bought to Adam, the 5 from the remaining to his brother. The apples she left with are 3. The number of apples she gave to Adam are
Like terms 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.
The solution of the equation 120x + 60 = 30(4x + 2) is
The linear equations with one variable are an equation which has only one variable and the highest power of the variable should be one. The linear equations in one variable having infinitely many solutions have same variable and constant terms on both the sides of the equation. On solving the equation, they will get cancelled and will give 0=0 as result.
The solution of the equation 120x + 60 = 30(4x + 2) is
The linear equations with one variable are an equation which has only one variable and the highest power of the variable should be one. The linear equations in one variable having infinitely many solutions have same variable and constant terms on both the sides of the equation. On solving the equation, they will get cancelled and will give 0=0 as result.
John says, “two times a number is subtracted from five results three”, the solution of the John equation is
Like terms 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.
John says, “two times a number is subtracted from five results three”, the solution of the John equation is
Like terms 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.
The equation among the following that have infinitely many solutions is
The linear equations with one variable is an equation which has only one variable and the highest power of the variable should be one. The linear equations in one variable having infinitely many solutions have same variable and constant terms on both the sides of the equation. On solving the equation they will get cancelled and will give 0=0 as result.
The equation among the following that have infinitely many solutions is
The linear equations with one variable is an equation which has only one variable and the highest power of the variable should be one. The linear equations in one variable having infinitely many solutions have same variable and constant terms on both the sides of the equation. On solving the equation they will get cancelled and will give 0=0 as result.
The solution of the equation 2.5x +1 =6 is
Like terms 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.
The solution of the equation 2.5x +1 =6 is
Like terms 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.
y = 4,
,
