The inequality 1 - 2(3e - 4) > 6 simplifies to e < 0.5. To graph it, draw a number line, place an open circle at 0.5, and shade everything to the left to represent the solution set.
To solve the inequality 1 - 2(3e - 4) > 6, first simplify the expression inside the parentheses and then apply the distributive property:
Multiply -2 by both 3e and -4 to get -6e + 8.
Simplify the inequality: 1 + 8 - 6e > 6.
Combine like terms: 9 - 6e > 6.
Subtract 9 from both sides: -6e > -3.
Divide both sides by -6, remembering to reverse the inequality symbol: e < 0.5.
Now we can graph this inequality on a number line:
Draw a number line and place a circle at 0.5, indicating that 0.5 is not included in the solution.
Shade the area to the left of 0.5, indicating all numbers less than 0.5 are included in the solution.