Question

How do you solve \[\dfrac{{4 + x}}{5} \le 8\]?

Answer 1

Hint: Here we will find the value of \[x\] by solving the given inequality. First, we will perform basic mathematical operations like multiplication, division, addition, and subtraction to simplify this inequality. A linear inequality is equality which has the highest degree of 1.

Complete step by step solution:
Given equation is \[\dfrac{{4 + x}}{5} \le 8\].
First, we will take the number 5 which is in the denominator of the LHS of the equation to the other side of the equation. Therefore, we get
\[ \Rightarrow 4 + x \le 8 \times 5\]
Multiplying the terms, we get
\[ \Rightarrow 4 + x \le 40\]
Now we will simply subtract number 4 from both sides of the above equation to get the value of \[x\]. Therefore, we get
\[ \Rightarrow 4 + x - 4 \le 40 - 4\]
\[ \Rightarrow x \le 36\]

Hence by solving the given equation i.e. \[\dfrac{{4 + x}}{5} \le 8\] we get the value of \[x\] as \[x \le 36\].

Additional information:
Here we have to note that while solving some complex type of equation we have to use the rule of BODMAS. We should apply the mathematical operations in a particular order which is given by the letters of BODMAS and letters of BODMAS are defined as B-Brackets, O-Of, D-Division, M-Multiplication, A-Addition, and S-Subtraction.

Note:
We should know the basic mathematical operations. The addition is the operation in which two numbers are combined to get the result. Subtraction is the operation that gives us the difference between the two numbers. Multiplication is the operation in which one number is added to itself for some particular number of times. The division is the operation in which the dividend is divided by the divisor to get the quotient along with some remainder where the dividend is the term or number which is to be divided.