Question

Solve the inequality. Graph and check your solution.

$10\ge y+4$

Short answer

The solution for the inequality is $y\le 6$.

Step-by-step solution

Step -1 - Apply the concept of Linear inequalities

In this type of inequality, Simply use the property of addition or subtraction of suitable number on both Left Hand Side & Right Hand Side to maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Step -2 – Find the value of n by solving the inequality

Since, the equality is $10\ge y+4$.

Here, to simplify this inequality, subtract $4$ to both side on the above

$\begin{array}{l}10\ge y+4\\ 10-4\ge y+4-4\\ 6\ge y\\ y\le 6\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, the expression is $y\le 6$.

So, this expression means that the value of y should be smaller than or equal to $6$.

So, Put $6,5,4,.....\&..so on$in $10\ge y+4$to check whether the inequality hold or not

Put $y=6$in inequality,

$\begin{array}{l}10\ge y+4\\ 10\ge 6+4\\ 10\ge 10\\ 10=10\end{array}$

It holds the equation

Again, put $y=5$ in equality

$\begin{array}{l}10\ge y+4\\ 10\ge 5+4\\ 10\ge 9\end{array}$

It also holds the inequality.

So, the expression $y\le 6$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $y\le 6$ to get the proper graphical representation to know the points.