Choose the correct solution graph for the inequality. 8x + 2 ≥ 26 or 4x – 6 ≤ –26
To determine the solution graph for the inequality 8x + 2 ≥ 26 or 4x – 6 ≤ –26, we need to solve each inequality separately and then identify the part of the number line that satisfies both inequalities.
Starting with the first inequality, 8x + 2 ≥ 26, we can isolate x by subtracting 2 from both sides:
8x + 2 - 2 ≥ 26 - 2
8x ≥ 24
Next, dividing both sides of the inequality by 8:
(8x)/8 ≥ 24/8
x ≥ 3
So, the first inequality, 8x + 2 ≥ 26, can be represented by x ≥ 3.
Now let's solve the second inequality, 4x – 6 ≤ –26. Adding 6 to both sides:
4x - 6 + 6 ≤ -26 + 6
4x ≤ -20
And dividing both sides by 4:
(4x)/4 ≤ -20/4
x ≤ -5
So, the second inequality, 4x - 6 ≤ –26, can be represented by x ≤ -5.
To identify the part of the number line that satisfies both inequalities, we need to find the overlapping region between x ≥ 3 and x ≤ -5. Since there is no overlap between these two conditions, there is no solution that satisfies both inequalities.
Therefore, the correct solution graph for the given inequality is an empty graph.
The table shows the relationship between two variables. Which selection describes the relationship? x y 1 5 2 –1 3 –7 4 –13
To determine the relationship between the variables x and y in the table, we can observe the pattern in the values.
When x increases by 1 from 1 to 2, y decreases by 6 from 5 to -1.
When x increases by 1 from 2 to 3, y decreases by 6 from -1 to -7.
When x increases by 1 from 3 to 4, y decreases by 6 from -7 to -13.
From this pattern, it is evident that as x increases by 1, y decreases by 6.
Therefore, the relationship between the variables x and y can be described as y = -6x.