Exercise 1 Page 52

Consider the given inequality.

2 x + 3 < x - 1

To solve this using a calculator, we begin by pressing

Y =

and writing the inequality in the first row.

Having entered the inequality in the calculator, we now push $GRAPH$ to draw it.

Notice that the graph is to the left of

- 4 .

Since the original inequality is strict, we will use the symbol

< .

x < - 4

We obtained that each number less than

- 4

is the solution of the inequality.

Different Approach

We can solve the given inequality without using calculator. To do so, we should first gather all of the variable terms on one side of the inequality and all of the constant terms on the other side using the Properties of Inequality. In this case, we need to use the Subtraction Property of Inequality. Let's do it!

2 x + 3 < x - 1

$LHS - x < RHS - x$

2 x + 3 - x < x - 1 - x

Subtract terms

x + 3 < - 1

$LHS - 3 < RHS - 3$

x + 3 - 3 < - 1 - 3

Subtract terms

x < - 4

Solving the inequality algebraically, we also got that each number less than

- 4

is the solution of the inequality.