5x - 7 > -14 + 3x Subtract 3x from both sides: 2x - 7 > -14 Add 7 to both sides: 2x > -7
Next inequality: -4x + 5 > 29 + 2x Add 4x to both sides: 5 > 29 + 6x Subtract 29 from both sides: -24 > 6x Divide by 6 (note: since dividing by a negative number, the inequality sign will reverse): -4 < x
Putting both inequalities together, we have: -4 < x < -7
Therefore, the solution to the system of inequalities is x is a real number between -7 and -4, excluding -7 and -4.
Let's simplify the inequality step by step:
5x - 7 > -14 + 3x
Subtract 3x from both sides:
2x - 7 > -14
Add 7 to both sides:
2x > -7
Next inequality:
-4x + 5 > 29 + 2x
Add 4x to both sides:
5 > 29 + 6x
Subtract 29 from both sides:
-24 > 6x
Divide by 6 (note: since dividing by a negative number, the inequality sign will reverse):
-4 < x
Putting both inequalities together, we have:
-4 < x < -7
Therefore, the solution to the system of inequalities is x is a real number between -7 and -4, excluding -7 and -4.