Solve the inequality. Expression solution set using interval notation and graph the solution set using a number line. -15x+3<_-3(4x-7)
Thats supposed to be a greater than or equal to sign lol
solve just like an equation:
-15x+3 >= -3(4x-7)
-15x+3 >= -12x+21
-18 >= 3x
-6 >= x
"≥" can be obtained by using ">" key along with "option" key.
To solve the inequality -15x + 3 ≥ -3(4x - 7), we can proceed as follows:
Step 1: Distribute the -3 on the right side:
-15x + 3 ≥ -12x + 21
Step 2: Combine like terms by subtracting -12x from both sides:
-15x + 12x + 3 ≥ 21
Simplifying, we have:
-3x + 3 ≥ 21
Step 3: Subtract 3 from both sides:
-3x + 3 - 3 ≥ 21 - 3
Simplifying, we have:
-3x ≥ 18
Step 4: Divide by -3 (remembering to reverse the inequality when dividing by a negative number):
(-3x) / -3 ≤ 18 / -3
Simplifying, we have:
x ≤ -6
In interval notation, the solution set is (-∞, -6]. To graph the solution set on a number line, you would mark a closed circle at -6 and shade the region to the left of -6, indicating that all values less than or equal to -6 satisfy the inequality.
To solve the inequality -15x + 3 ≥ -3(4x - 7), we will need to simplify the expression and isolate the variable x.
Let's start by distributing -3 to the terms inside the parentheses:
-15x + 3 ≥ -12x + 21
Next, we can combine like terms by subtracting -12x from both sides of the inequality:
-15x + 12x + 3 ≥ 21
Combining like terms, we have:
-3x + 3 ≥ 21
Now, we can isolate the variable x by subtracting 3 from both sides of the inequality:
-3x + 3 - 3 ≥ 21 - 3
Simplifying further gives:
-3x ≥ 18
To solve for x, we need to divide both sides of the inequality by -3. However, since we are dividing by a negative number, we need to reverse the inequality symbol:
x ≤ 18 / -3
Simplifying the right side of the equation:
x ≤ -6
Therefore, the solution to the inequality -15x + 3 ≥ -3(4x - 7) is x ≤ -6.
To represent this solution on a number line, we can plot a closed circle at -6 and shade everything to the left of it. This represents all values of x that satisfy the inequality. The final representation on the number line is:
```
<----(-)===|----------------
-10 -6 0
```
In interval notation, the solution set is (-∞, -6].