Question

Solve the inequality and show the graph of the solution on the number line: $3x - 2 < 2x + 1$.

Answer 1

Hint: In order to solve this question, we will first try to get the variables on one side and the constants on the other side, and then we will represent it on the number line. Also, we have to remember that if there is a point at which equality occurs, then we will represent with a dark circle, otherwise, we will represent the corner point by a hollow circle.

Complete step-by-step solution -
In this question, we have been asked to solve an inequality, that is, $3x - 2 < 2x + 1$ and we have been asked to represent it on the number line. To solve this, we will first take the variables on to the left-hand side and the constants on the right side. For that, we will subtract 2x from both sides of the equation. So, we will get,
$3x - 2 - 2x < 2x + 1 - 2x$
And we know that only like terms show addition and subtraction properties, so we get,
$x - 2 < 1$
Now, we will add 2 to both sides of the equation. So, we get,
$x - 2 + 2 < 1 + 2$
Which can further be written as $x < 3$.
Hence, we can say that the solution of the equation, $3x - 2 < 2x + 1$ is $x < 3$. We can represent it on the number line as,

We have represented point 3 by a hollow circle, because the value of x is less than 3, but not equal to 3.

Note: While solving this question, we need to be very careful while doing the calculations, because we may make a calculation mistake in a hurry. Also, we need to remember that while drawing the number line that when the corner point is not in range, then we represent them by open or hollow circles.