Solve the compound inequality. Graph the solution.
6x – 4 < –34 or 3x + 10 > 10
To solve the compound inequality 6x - 4 < -34 or 3x + 10 > 10, we can solve each inequality separately and then combine their solutions.
For the first inequality, 6x - 4 < -34, we can add 4 to both sides to isolate the variable:
6x - 4 + 4 < -34 + 4
6x < -30
Next, we divide both sides by 6 to solve for x:
6x/6 < -30/6
x < -5
For the second inequality, 3x + 10 > 10, we can subtract 10 from both sides to isolate the variable:
3x + 10 - 10 > 10 - 10
3x > 0
Next, we divide both sides by 3 to solve for x:
3x/3 > 0/3
x > 0
Combining the solutions from both inequalities, we have -5 < x < 0. This means x can take any value between -5 and 0 (exclusively).
To graph the solution, we represent the interval -5 < x < 0 on a number line. We use an open circle at -5 and an open circle at 0, to indicate that these values are excluded from the solution. Then, we shade the region between -5 and 0 to represent the values that satisfy the inequality.
Below is the graph of the solution on a number line:
-6 --5 --4 --3 --2 --1 --0 --1 --2 --3 --4 --5 --6
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