Solving the Inequality -5 ≤ 1 – 3x ≤ 4 Step-by-Step: Find values of x on a Number Line

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).

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