Final answer:
To solve the inequality -7x + 14 > -3x - 6, eliminate terms to simplify and then isolate the variable. Ultimately, the solution is 'x < 5', meaning all values of x that are less than 5 satisfy the inequality.
Step-by-step explanation:
The given inequality is -7x + 14 > -3x - 6. To solve it, you would first eliminate terms on both sides to simplify the algebra. This involves moving all the x terms to one side and the constant terms to the other side.
To do this, add 3x to both sides:
-7x + 14 + 3x > -3x - 6 + 3x
-4x + 14 > -6
Next, subtract 14 from both sides:
-4x + 14 - 14 > -6 - 14
-4x > -20
Now, divide both sides by -4. Remember, dividing by a negative number will reverse the inequality sign:
x < 5
The solutions to the inequality are all the values of x that are less than 5. Check the answer by plugging in a number less than 5 for x and confirming that the inequality holds true.