Question

How do you solve \[1.75x+2.50x=165\]?

Answer 1

Hint: From the given question we have an equation \[1.75x+2.50x=165\] to solve.
We can solve the given equation from the question by using addition. Here in the equation, we have only one variable i.e., \[x\]. so, by doing addition to the left-hand side we will get only one variable term and then by applying simple transformations to the given equation, we get the equation simplified and then we can solve the equation very easily.

Complete step by step solution:
From the question given, we have been given that,
\[1.75x+2.50x=165\]
As we have already discussed earlier, we have to make addition to the left-hand side equation to get it simplified.
In the left-hand side of the above equation, we can clearly see that there is a variable common in both the terms.
So, we know that if the variable is common in the terms, we can simply add the constants of the variables.
Take \[x\] as common in left hand side of the equation then we will get equation as
\[\Rightarrow x\left( 1.75+2.50 \right)=165\]
Now, simplify the above equation by adding the two decimal numbers which are present in the left-hand side of the equation
By adding we get
\[\Rightarrow x\left( 4.25 \right)=165\]
\[\Rightarrow 4.25x=165\]
Now, Shift \[4.25\] from the left hand side of the equation to the right-hand side of the equation. By shifting \[4.25\] from left hand side of the equation to the right-hand side of the equation, we get
\[\Rightarrow x=\dfrac{165}{4.25}\]
By simplifying this, we get
\[\Rightarrow x=38.823\]

Note: Students should be well aware of the addition of two decimal numbers.
\[\Rightarrow x=\dfrac{165}{4.25}\]
Students should know how to divide with the decimal number in the above step. Students should be very conscious while doing the calculation with the decimal numbers.