Graph the inequality and graph its solution
-2x>8 or 3x+1_> 7
Im clueless on how to solve this equation
You are looking for a region of the x domain that satifies both equation. Solve each..
first
-2x>8
2x<=-8
x<=-4
so do the same on the second equation, then plot the allowed domain of x which satisfies both equations.
To graph the inequality -2x > 8 or 3x + 1 ≥ 7, we need to follow a few steps:
Step 1: Solve each inequality separately.
-2x > 8 (Inequality 1)
3x + 1 ≥ 7 (Inequality 2)
Let's start with Inequality 1:
-2x > 8
To solve this inequality, we need to isolate the variable x. First, divide both sides by -2, remembering that when dividing by a negative number, we flip the inequality sign:
-2x/(-2) < 8/(-2)
x < -4
So the solution to Inequality 1 is x < -4.
Next, let’s move on to Inequality 2:
3x + 1 ≥ 7
To solve this inequality, we need to isolate the variable x. First, subtract 1 from both sides:
3x + 1 - 1 ≥ 7 - 1
3x ≥ 6
Now divide both sides by 3:
(3x)/3 ≥ 6/3
x ≥ 2
So the solution to Inequality 2 is x ≥ 2.
Step 2: Graph each solution on a number line.
To graph x < -4, start at -4 and draw an open circle (since it is less than, not less than or equal to), then shade to the left of that point to show all the possible solutions.
To graph x ≥ 2, start at 2 and draw a closed circle (since it is greater than or equal to), then shade to the right of that point to show all the possible solutions.
Step 3: Combine the graphs.
Since we have two separate inequalities, the graph of the solution to the original inequality will combine both graphs. Thus, we shade the region that satisfies either of the inequalities. In this case, we shade to the left of -4 and to the right of or on 2.
The final graph will show a shaded area between -∞ (negative infinity) and -4, and another shaded area between 2 and +∞ (positive infinity). The shaded regions represent the possible solutions for the given inequality.