Solve the inequality. Graph and check your solution.
x / 3 < - 2
To solve the inequality x/3 < -2, we will follow these steps:
Step 1: Multiply both sides of the inequality by 3 (because the coefficient of x is 3 in the denominator).
3 * (x / 3) < 3 * (-2)
x < -6
So the solution to the inequality is x < -6.
To graph the solution on a number line, we will represent all the numbers less than -6. We can do this by drawing an open circle at -6 and shading the line to the left of -6.
Now let's check the solution by substituting a value less than -6 into the original inequality:
Let's pick x = -7.
Plugging x = -7 into the inequality:
(-7) / 3 < -2
Simplifying the inequality:
-7/3 is indeed less than -2.
Since the statement is true, x = -7 satisfies the inequality.
Therefore, the solution is correct.
To solve the inequality x/3 < -2, we can multiply both sides of the inequality by 3 to eliminate the fraction. However, since we are multiplying by a negative number, we need to reverse the inequality sign.
Multiplying both sides by 3 and reversing the inequality sign, we get:
x < -6
To graph this solution, we need to draw a number line and mark the point -6. Since the inequality is less than, we shade the part of the number line to the left of -6.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
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x< -6
To check the solution, we can plug in a value from the shaded region into the inequality and see if it holds true. Let's choose x = -7.
(-7/3) < -2
-7/3 is approximately -2.33
-2.33 is less than -2, so the inequality holds true.
Therefore, the solution to the inequality x/3 < -2 is x < -6.
To solve the inequality, x/3 < -2, follow these steps:
Step 1: Multiply both sides of the inequality by 3 to eliminate the fraction:
(x/3) * 3 < -2 * 3
x < -6
Step 2: Graph the solution on a number line. Draw an open circle at -6 and shade the region to the left of -6.
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Step 3: Check the solution by substituting a value from the shaded region into the original inequality.
Let's choose x = -7 (a value in the shaded region).
(-7/3) < -2
-7/3 is approximately -2.333, which is less than -2.
Since the inequality is true when x = -7, the solution is correct.
Thus, the solution to the inequality x/3 < -2 is x < -6.