Question

How do you solve \[4x + 5 < 21\] ?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. The given equation is a linear equation as there is a constant variable involved and to solve the given inequality, combine all the like terms and then simplify the terms to get the value of \[x\].

Complete step by step solution:
Let us write the given inequality
\[4x + 5 < 21\]
To find the value of \[x\], Subtract 5 from both sides of the inequality as
\[4x + 5 - 5 < 21 - 5\]
As we know that the value -5 and +5 implies to zero, hence we get
\[4x < 16\]
Now dividing both sides by 4, as
\[\dfrac{{4x}}{4} < \dfrac{{16}}{4}\]
\[x < \dfrac{{16}}{4}\]
After simplifying we get the value of \[x\] as
\[x < 4\]
Therefore, the value of \[x\] in inequality form is \[x < 4\].

Additional information:
Equations that have more than one unknown can have an infinite number of solutions, finding the values of letters within two or more equations are called simultaneous equations because the equations are solved at the same time.

Solving simultaneous equations by elimination: The most common method for solving simultaneous equations is the elimination method which means one of the unknowns will be removed from each equation. The remaining unknown can then be calculated. This can be done if the coefficient of one of the letters is the same.

Solving simultaneous equations by Substitution: The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equations gets transformed into one linear equation with only one variable, which can then easily be solved.


Note: The key point to solve this type of equation is to combine all the like terms i.e., finding out the common term and evaluate for the variable asked. As we know that Simultaneous equations are two equations, each with the same two unknowns and are "simultaneous" because they are solved together.