Question

How do you solve the inequality \[3x-4<10?\]

Answer 1

Hint: Firstly eliminate fraction by multiplying all terms by least common denominator all the terms.
Simplify by combining like terms on each side of the inequality. Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

Complete step by step solution:
As we know that here you have to solve the inequality \[3x-4<10.\]
\[3x-4<10\]
Above isolate \[3x\] by adding \['4'\] to both sides of the inequality. Therefore, the inequality equation will be,
\[3x-4+4<10+4\]
As you can see that \['-4'\] and \['+4'\] on the left side will get canceled by each other. Therefore the modified inequality equation will be.
\[3x<14\]
Divide both side of above equation by \['3'.\]
\[\dfrac{3x}{3}<\dfrac{14}{3}\]
Here above in the left side \[\dfrac{3x}{3}\] the \['3'\] of numerator and denominator will get canceled by each other.
\[\dfrac{3x}{3}<\dfrac{14}{3}\]
Hence the modified inequality will be \[x<\dfrac{14}{3}.\]

Therefore \[x<\dfrac{14}{3}\] is the solution.

Note: An inequality if similar to an equation except that the statement is that two expressions have a relationship other than equality, such as \[<,\le ,>or\ge .\] To solve an inequality means to find the all values of the variable that make the inequality true.