Solve using the multiplication principle
-7x <_ 35
the sign is an inequality equal greater or lesser than sign
would I substitute the sign for an equal sign and then divide 35 by -7
x=-5
-7 x -5= 35
how would I write the solution set? can someone please help me?
can someone please help me?
-7x <_ 35 or
-7x ≤ 35 , divide by -7
x ≥ -5
remember that if you multiply or divide by a negative number, the sign of inequality has to be reversed.
To solve the inequality -7x ≤ 35 using the multiplication principle, you need to divide both sides of the inequality by -7. However, keep in mind that when you divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.
Let's go through the steps together:
1. Start with the inequality: -7x ≤ 35
2. Divide both sides of the inequality by -7, but remember to reverse the inequality sign:
(-7x)/-7 ≥ 35/-7
This gives: x ≥ -5
So, the solution to the inequality is x ≥ -5.
To represent the solution set, you can write it as an interval or using set notation:
- Interval notation: [ -5, ∞ )
This indicates that x is greater than or equal to -5 and can take any value greater than -5.
- Set notation: {x | x ≥ -5}
This represents the set of all values of x that are greater than or equal to -5.