Question
Solve 0.9x+5.1x - 7 =2(2.5x - 3). How many solutions does the equation have ?
Hint:
When a given equation has only 1 value that can be substituted for the variable which will satisfy the given equation, the said equation has only 1 solution. i.e. after simplifying the equation, we will get a single value as the solution for x.
We will simplify the given equation and the number of values we get for the variable.
The correct answer is: The given equation i.e. 0.9x + 5.1x - 7 = 2(2.5x - 3) can be classified as an equation with only one solution
Step-by-step solution:-
Simplifying the given equation i.e. 0.9x+5.1x -7 =2(2.5x-3), we get-
0.9x + 5.1x - 7 = 2(2.5x - 3)
∴ 0.9x + 5.1x - 7 = 5x - 6 .................................. (Opening the brackets and multiplying 2 with the entire expression on RHS)
∴ 0.9x + 5.1x - 5x = -6 + 7 .................................. (Taking variables and constants on either sides of the variable)
∴ x = 1
Since after simplifying the given equation, we get a single value of x i.e. 1 that will satisfy the given equation, we can conclude that the given equation has 1 solution.
Final Answer:-
∴ The given equation i.e. 0.9x + 5.1x - 7 = 2(2.5x - 3) can be classified as an equation with only one solution.
Related Questions to study
Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.
Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.
¶Types of Expression
1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.
¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.
Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.
Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.
¶Types of Expression
1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.
¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.
