Question

You are travelling by train. Your are allowed two carryon bags, each maximum weight of $50$ pounds. You have two bags: one that weighs $14$ pounds and one that weighs $21$ pounds.

1. Write and solve an inequality that represents the weight wof personal belonging you can add to the first bag without exceeding the weight limit.
2. Write and solve an inequality that represents the weight wof personal belonging you can add to the second bag without exceeding the weight limit.

Short answer

a.The inequality of the first bag is $w\le 36$.

b.The inequality of the second bag is $w\le 29$.

Step-by-step solution

a. 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 and also understand the question words.

Step -2 – Finding the inequality by explaining the question

Since, the maximum weight of the bag is $50$ pound.

And, Weight of the first bag is $14$pound.

Now, the equation should be like that the weight of the personal belonging and the weight of the bag combinedly should be less than or equal to $50$pound.

Step- 3 – Make the expression of the inequality and solve the inequality

Now, Let the weight of the personal belonging to be w.

So, the inequality can be represented by: $w+14\le 50$

Now, solving the inequality, subtracting $14$to both side of the equation

Graphical Interpretation

Following is the graph of the expression $w\le 36$ to get the proper graphical representation to know the points.

b.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 and also understand the question words.

Step -2 – Finding the inequality by explaining the statement

Since, the maximum weight of the bag is $50$ pound.

And, Weight of the first bag is $21$ pound.

Now, the equation should be like that the weight of the personal belonging and the weight of the bag combinedly should be less than or equal to $50$pound.

Step- 3 – Make the expression of the inequality and solve the inequality

Now, Let the weight of the personal belonging to be w.

So, the inequality can be represented by: $w+21\le 50$

Now, solving the inequality, subtracting $21$ to both side of the equation

$\begin{array}{l}w+21\le 50\\ w+21-21\le 50-21\\ w\le 29\end{array}$

Graphical Interpretation

Following is the graph of the expression $w\le 29$ to get the proper graphical representation to know the points.