Question

What is the solution of the inequality shown below? c+3>8

Answer 1

Answer:

  c > 5

Step-by-step explanation:

The properties of equality can be used to solve inequalities. Attention needs to be paid to ordering.

Application

We can subtract 3 from both sides to solve this.

  c +3 > 8 . . . . . . given

  c +3 -3 > 8 -3 . . . . subtract 3 from both sides

  c > 5 . . . . . . . . . simplify

The solution is c > 5.

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Additional comment

Adding or subtracting a value to a number on a number line is equivalent to shifting it right or left. It does not change ordering.

Multiplying or dividing by a positive number is equivalent to expanding or compressing the distance from zero. It does not change ordering.

Multiplying or dividing by a negative number reflects the value across the origin, in addition to expanding or compressing the distance from zero. This reflection reverses the left-right ordering. For example, -2 < -1, but 2 > 1. (Both numbers multiplied by -1.)

As long as you're aware of the effect on ordering, you can use any of the properties of equality to solve inequalities.