What number line represents the values of x that satisfy the inequality -5 <= 1 - 3x <= 4 ?
To find the number line that represents the values of x that satisfy the inequality -5 ≤ 1 – 3x ≤ 4, we need to solve the inequality step by step
To find the number line that represents the values of x that satisfy the inequality -5 ≤ 1 – 3x ≤ 4, we need to solve the inequality step by step.
Step 1: Start by isolating the variable x in the middle of the inequality, which is 1 – 3x.
1 – 3x ≤ 4
Subtract 1 from both sides of the inequality:
-3x ≤ 3
Step 2: To isolate x, divide both sides of the inequality by -3. Here, we need to be cautious because dividing by a negative number reverses the inequality.
When dividing by a negative number, we flip the inequality signs:
-3x/(-3) ≥ 3/(-3)
This simplifies to:
x ≥ -1
Step 3: Now we need to solve the other part of the inequality to find the lower bound for x.
-5 ≤ 1 – 3x
Subtract 1 from both sides:
-5 – 1 ≤ -3x
-6 ≤ -3x
To get x alone, divide both sides of the inequality by -3. Again, remember that dividing by a negative number reverses the inequality sign:
-6/(-3) ≥ -3x/(-3)
This simplifies to:
2 ≥ x
or
x ≤ 2
Step 4: Take the intersection of the two intervals we obtained in Step 2 and Step 3.
The solution to the inequality -5 ≤ 1 – 3x ≤ 4 is:
-1 ≤ x ≤ 2
Step 5: Finally, we represent the solution on a number line. Draw a line with an arrow to the right and label it with numbers from left to right. Place a closed dot at -1 and a closed dot at 2 to represent the boundaries. Shade the region between -1 and 2 to show that all numbers within that range satisfy the inequality.
———————————————–
-∞ —|-1——0——-1——2|— ∞
In this example, the values of x that satisfy the inequality are between -1 and 2 (including -1 and 2).
More Answers:
[next_post_link]