compound inequality
write the solution set using interval notation and graph
-7x+1>=15 or 5x+3>=-17
-1 -1 -3 -3
-7x/-7>=14/-7 5x/5>=-20/5
x>=-2 x>=-4
{-2,sideways8) {-4,sideways8)
On my graph I have a { at -2
Does someone know how to do this?
-7x+1>=15
-7x ≥ 14 now divide by -7 and switch the inequality sign
x ≤ -2
or
5x+3>=-17
5x ≥ -20 divide by 5
x ≥ -4
so x ≤ -2 OR x ≥ -4
Since you used OR the results would cover the entire number line, and the solution would be any real number
(try any number, it would satisfy either the first OR the second of your inequalities)
Are you sure the two statements weren't separated by the world "and" ?
To solve the compound inequality -7x+1>=15 or 5x+3>=-17, we need to solve the individual inequalities separately and then combine the solutions.
Let's start with the first inequality: -7x+1>=15.
Begin by subtracting 1 from both sides to isolate the variable:
-7x >= 14
Next, divide both sides by -7. Remember that when you divide or multiply both sides of an inequality by a negative number, you need to reverse the direction of the inequality symbol:
x <= -2
So the solution for the first inequality is x <= -2.
Now let's focus on the second inequality: 5x+3>=-17.
Subtract 3 from both sides:
5x >= -20
Divide both sides by 5:
x >= -4
Therefore, the solution for the second inequality is x >= -4.
To find the solution set for the compound inequality, we need to find the values of x that satisfy either of the individual inequalities.
In this case, the solution set can be written using interval notation as the union of the two separate solution sets:
[-∞, -4] U [-2, ∞)
To graph the solution on a number line, plot an open circle at -4, indicating that -4 is not included in the solution set. Then, draw an arrow to the left to represent all the values less than -4. Next, plot a closed circle at -2, indicating that -2 is included in the solution set. Finally, draw another arrow to the right to represent all the values greater than -2.