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Problem 1

# Find the graphical solution of each inequality. $$4 x-8<0$$

Expert verified
The graphical solution of the inequality $$4x - 8 < 0$$ includes all values of x less than 2, represented as $$(-∞, 2)$$.
See the step by step solution

## Step 1: Simplify the inequality

First, we need to simplify the inequality. We have the inequality: $$4x - 8 < 0$$ We want to isolate the variable x, so we need to add 8 to both sides and then divide by 4.

## Step 2: Identify the critical point

Now that we have isolated x, we have: $$x < 2$$ The critical point is the value of x where the inequality changes from true to false or vice versa. In this case, the critical point is 2. Now we need to test the inequality on either side of this critical point.

## Step 3: Test the inequality

We will test the inequality with a value less than 2 and a value greater than 2. If we choose a value less than 2, like 1: $$1 < 2$$ This is true, so all values less than 2 satisfy the inequality. If we choose a value greater than 2, like 3: $$3 < 2$$ This is false, so all values greater than 2 do not satisfy the inequality.

The graphical solution of the inequality $$4x - 8 < 0$$ will include all values of x less than 2. In interval notation, this is represented as $$(-∞, 2)$$. On a number line, the solution set would be an open circle at the critical point (2) with an arrow pointing to the left towards negative infinity.

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