a number-line depicts 1.5 going to the right all the way to 10.
Preston solved in inequality and graph the solution on the number line. which of the following inequalities did he solve?
answer: 2.1x + 5.6 ≥ 8.75
can you break down this answer and explain why it equals 1.5?
To explain why the inequality 2.1x + 5.6 ≥ 8.75 represents 1.5 on the number line, we need to solve the inequality for x.
Starting with 2.1x + 5.6 ≥ 8.75, we can isolate the variable x by subtracting 5.6 from both sides of the inequality:
2.1x + 5.6 - 5.6 ≥ 8.75 - 5.6
2.1x ≥ 3.15
Next, we can divide both sides of the inequality by 2.1 (the coefficient of x) to solve for x:
2.1x / 2.1 ≥ 3.15 / 2.1
x ≥ 1.5
This means that any value of x greater than or equal to 1.5 will satisfy the inequality.
Now, let's examine how this translates to the number line. We are given that 1.5 is depicted on the number line and the inequality represents all the numbers to the right of 1.5.
So, if we start from 1.5 and move to the right along the number line, we will encounter all the values that satisfy the inequality. In other words, all the numbers greater than or equal to 1.5, including 1.5 itself, will make the inequality true.
Hence, the inequality 2.1x + 5.6 ≥ 8.75 represents 1.5 on the number line.