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How Do You Solve and Graph a Two-Step Inequality?

Solve this inequality for t: 74 - 0.8t < 10
Write the solution in set-builder notation and graph the solution set on a number line.

Summary

  1. Subtracting 74 from the left side cancels out the '74' and gives us the 't' term by itself
  2. Subtracting 74 from '10' on the right side will give us '-64'
  3. Dividing by -0.8 gives us 't'
  4. The inequality symbol flips when dividing by a negative
  5. Open circles represent '<' or '>' symbols
  6. Notice that an arrow points in the same direction as the inequality symbol!

Notes

    1. This will allow us to solve for our variable 't'
    1. This will allow us to solve for our variable 't'
    1. In other words, 74 is being added to the inequality
    1. Subtracting '74' from the left side will cancel out the '74' and give us '-0.8t' by itself
    2. Subtracting '74' from '10' on the right side will give us '-64'
    3. 10-74 = -64
    4. -0.8t < -64
    1. This will help us get 't' by itself on the left side
    1. The original inequality has -0.8 being multiplied by 't'
    1. The original inequality has -0.8 being multiplied by 't'
    2. The opposite of multiplication is division
    3. Dividing the left side by '-0.8' will cancel out the multiplication by '-0.8', leaving us with 't' alone
    4. -0.8t/-0.8 = 1
    5. Dividing '10' on the right side by '-0.8' will give us '80'
    6. -64/-0.8 = 80
    1. With inequalities, if we divide or multiply by a negative number, the inequality sign needs to be flipped
    2. Our first inequality is now 't>80'
    1. Our first inequality is now 't>80'
    1. Our answer was the inequality 't>80'
    1. Opening up your set just means to start with a curly brace, '{'
    2. "Such that" = '|'
    3. So we start with '{t|'
    1. Our answer was the inequality 't>80'
    2. The '>' symbol means GREATER THAN
    1. Close your set with a curly brace, '}'
    1. Our answer was the inequality 't>80'
    1. We chose these numbers because they were on both sides of 80, the number in our answer
    1. 80 was the number in our answer
    1. Our answer was the inequality 't>80'
    2. Open circles represent '<' or '>' symbols
    3. Notice that the GREATER THAN symbol, '>', points to the right, the same direction as the arrow in our graph