Solve the following inequality. Graph and check your solution.
7m < 56
To solve the given inequality 7m < 56, you can follow these steps:
Step 1: Divide both sides of the inequality by 7.
(7m)/7 < 56/7
m < 8
Therefore, the solution to the inequality is m < 8.
To graph the solution, you can draw a number line and mark the value 8 with an open circle. Then shade the region to the left of 8 to represent all values of m that are less than 8. This indicates that m can be any value smaller than 8, but not equal to 8.
To check your solution, you can pick a value smaller than 8, say m = 5, and substitute it into the original inequality:
7m < 56
7(5) < 56
35 < 56
Since 35 is indeed less than 56, it satisfies the inequality. Thus, the solution m < 8 is valid.
To solve the inequality 7m < 56, we need to divide both sides of the inequality by 7.
Dividing both sides by 7, we get:
m < 8
Now let's graph the solution on a number line.
On the number line, we mark a point at 8 but leave it open (not filled in) because m is less than 8, not equal to 8.
---|---|---|---|---|---|---|---|---|
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
The shaded area on the left side of the point represents the solution to the inequality, m < 8.
To check our solution, we can pick a value of m that is less than 8, such as m = 5.
Substituting m = 5 into the original inequality, we get:
7(5) < 56
35 < 56
Since 35 is less than 56, the inequality holds true for m = 5.
Therefore, the solution to the inequality 7m < 56 is m < 8.
To solve the inequality 7m < 56, we need to isolate the variable m.
Divide both sides of the inequality by 7:
(7m)/7 < 56/7
This simplifies to:
m < 8
Now let's graph the solution on a number line:
-∞ ------------------------------------ 8 ------------------------------------ +∞
The solution to the inequality is all values of m that are less than 8 but do not include 8. So, the interval notation for the solution is (-∞, 8).
To check the solution, we can choose a value for m that is less than 8 and substitute it into the original inequality to see if it is true. Let's choose m = 7.
7m < 56
7(7) < 56
49 < 56
Since 49 is less than 56, the inequality is true. Therefore, the solution m < 8 is correct.