Solve the inequality, and graph the solution on a number line
5x -5 < 5 (x-3)
To solve the inequality 5x - 5 < 5(x - 3), we need to distribute the 5 on the right side of the inequality:
5x - 5 < 5x - 15.
Next, we can simplify the inequality:
5x - 5 < 5x - 15
-5 < -15.
This inequality is not true since -5 is not less than -15. Therefore, there are no solutions to the inequality 5x - 5 < 5(x - 3).
Graphically, this means that there are no numbers on the number line that satisfy the inequality.
To solve the inequality 5x - 5 < 5(x - 3), we can start by simplifying both sides of the inequality:
5x - 5 < 5x - 15
Next, let's isolate the variable on one side of the inequality. We can do this by subtracting 5x from both sides:
-5 < -15
Since this inequality is true for any value of x, we can say that x can be any real number. In other words, there are no restrictions on the value of x.
Now, let's graph this solution on a number line:
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Since there are no restrictions on the value of x, we indicate this on the number line by shading the entire line. We use an open circle at each end to show that the line goes on indefinitely without any specific endpoints. Hence, the graph of the solution is a number line with shading covering the entire line and open circles at each end.
To solve the inequality 5x - 5 < 5(x - 3), we need to simplify the expression and isolate the variable x.
Let's start by expanding the right side of the inequality:
5x - 5 < 5x - 15
Now we can simplify the equation by subtracting 5x from both sides:
-5 < -15
Since -5 is not less than -15, this inequality is not true. Thus, there are no values of x that satisfy this inequality.
When we graph the solution on a number line, we will have an empty number line without any marks, indicating that there are no values that satisfy the inequality.