Directions:Solve and explain the inequality using words.Tell which wa shading goes.
Problem:
x+3=>2x+1 and -4x<-8
-4x<-8
The first inequality can be rewritten
x <= 2 In words, x is less than or equal to 2.
You can get that by subtracting x+1 from both sides.
The second inequality can be rewritten
x>2
You get that by dividing both sides by -4 and reversing the > sign.
Both inequalities cannot be satisfied at the same time in this case.
To solve and explain the first inequality, x + 3 ≥ 2x + 1, we first need to isolate the variable x on one side of the inequality sign.
Subtracting 2x from both sides, we get x - 2x + 3 ≥ 2x - 2x + 1, which simplifies to -x + 3 ≥ 1.
Next, subtracting 3 from both sides, we have -x + 3 - 3 ≥ 1 - 3, yielding -x ≥ -2.
We need to flip the inequality sign to solve for x, so we divide both sides by -1. However, when dividing or multiplying an inequality by a negative number, it requires flipping the inequality sign. Thus, we have x ≤ 2.
In words, this means that x is less than or equal to 2. When graphing this inequality on a number line, we shade to the left of 2, including the point 2, since it satisfies the inequality.
Moving on to the second inequality, -4x < -8, we want to isolate x again. To do this, we divide both sides by -4, while also flipping the inequality sign, as we are dividing by a negative number.
Dividing -4x by -4, we get x > 2. The negative signs cancel out, and we reverse the inequality sign.
In words, this means that x is greater than 2. When graphing this inequality on a number line, we shade to the right of 2, excluding the point 2, since it does not satisfy the inequality.
However, when we consider both inequalities together, we realize that they cannot be satisfied at the same time. On one hand, we have x ≤ 2, which includes the point 2. On the other hand, we have x > 2, which excludes the point 2. Thus, there is no overlap between the two shading regions, and there is no possible value for x that satisfies both inequalities simultaneously.