3x+2≥-7
To solve the inequality 3x + 2 ≥ -7, we need to isolate x.
First, subtract 2 from both sides of the inequality:
3x + 2 - 2 ≥ -7 - 2
Simplifying the expression:
3x ≥ -9
Now, divide both sides of the inequality by 3:
(3x)/3 ≥ -9/3
Simplifying the expression:
x ≥ -3
Therefore, the solution to the inequality 3x + 2 ≥ -7 is x ≥ -3.
Write the set in set-builder notation.
{1,3,5,7}
The set {1, 3, 5, 7} can be written in set-builder notation as:
{x: x is an odd integer between 1 and 7, inclusive}
Write the inequality in interval notation. Then graph the interval.
x≤-3or x>4
The inequality x ≤ -3 or x > 4 can be written in interval notation as:
(-∞, -3] ∪ (4, ∞)
To graph this interval, draw a number line and place a solid dot at -3 to represent the inclusive boundary. Then, draw an arrow pointing to the left to represent all values less than -3. Next, draw an open circle at 4 to represent the exclusive boundary. Finally, draw an arrow pointing to the right to represent all values greater than 4.
Here is a visual representation of the interval:
-----o------------------- >o------
-3 4
Solve the absolute value equation.
│8x -4│-8=3
To solve the absolute value equation │8x - 4│ - 8 = 3, we can first isolate the absolute value expression by adding 8 to both sides:
│8x - 4│ = 11
Now, we can split the equation into two separate cases, one with the positive value inside the absolute value symbol, and one with the negative value inside.
Case 1: 8x - 4 > 0
Now, solve for x:
8x - 4 = 11
Add 4 to both sides:
8x = 15
Divide both sides by 8:
x = 15/8
Case 2: -(8x - 4) > 0
Now, solve for x:
-8x + 4 = 11
Subtract 4 from both sides:
-8x = 7
Divide both sides by -8 (remember to change the sign of the inequality when dividing by a negative number):
x = -7/8
Therefore, the solutions to the absolute value equation │8x - 4│ - 8 = 3 are x = 15/8 and x = -7/8.
Solve the inequality. Write the solution in interval notation.
│7 - 3x│≤10
To solve the inequality │7 - 3x│≤10, we can split it into two separate cases, one with the absolute value expression greater than or equal to 10, and one with the absolute value expression less than or equal to 10.
Case 1: 7 - 3x ≥ 10
Now, solve for x:
-3x ≥ 3
Divide both sides by -3 (remember to change the direction of the inequality when dividing by a negative number):
x ≤ -1
Case 2: -(7 - 3x) ≥ 10
Now, solve for x:
-7 + 3x ≥ 10
Add 7 to both sides:
3x ≥ 17
Divide both sides by 3:
x ≥ 17/3
Therefore, the solutions to the inequality │7 - 3x│≤10 are x ≤ -1 and x ≥ 17/3.
In interval notation, this can be written as:
(-∞, -1] ∪ [17/3, ∞)
To solve the inequality 3x + 2 ≥ -7, you need to isolate the variable x, similar to solving an equation. Here's how to do it step by step:
Step 1: Start by subtracting 2 from both sides of the inequality to get the term with x isolated.
3x + 2 - 2 ≥ -7 - 2
3x ≥ -9
Step 2: Divide both sides of the inequality by 3 to solve for x. Remember, when dividing or multiplying by a negative number, you need to flip the direction of the inequality symbol.
3x/3 ≥ -9/3
x ≥ -3
So, the solution to the inequality 3x + 2 ≥ -7 is x ≥ -3.