Question

How do you solve \[4x - 5 < 3x + 7\] ?

Answer 1

Hint: Here we need to solve for \[x\], if the equation consists of two variables \[x\] and y, hence to solve for both variables we can use substitution method to get both the values, but we need to solve only for \[x\], hence we can solve by taking \[x\] common from both LHS and RHS part we can find the solution. 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
\[4x - 5 < 3x + 7\]
Move all the terms containing \[x\] from RHS to LHS of the inequality, hence we get
\[4x - 5 - 3x < 7\]
As we can see that the LHS terms contains \[x\] terms, combine and simplify i.e., subtract \[3x\] from \[4x\] we get
\[x - 5 < 7\]
We need to find the value of \[x\], move all the terms which doesn’t contain \[x\] term to RHS of inequality we get
\[x < 7 + 5\]
\[x < 12\]

Therefore, the value of \[x\] in inequality form is \[x < 12\].

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.