To solve the first inequality:
3x + 4 ≤ -x + 12Add x to both sides:3x + x + 4 ≤ 124x + 4 ≤ 12Subtract 4 from both sides:4x ≤ 8Divide by 4:x ≤ 2
So the solution for the first inequality is x ≤ 2.
To solve the second inequality:
5x - 7 < 7x + 3Subtract 5x from both sides:-7 < 2x + 3Subtract 3 from both sides:-10 < 2xDivide by 2:-5 < x
So the solution for the second inequality is x > -5.
Therefore, the solutions to the system of inequalities are -5 < x ≤ 2.
To solve the first inequality:
3x + 4 ≤ -x + 12
Add x to both sides:
3x + x + 4 ≤ 12
4x + 4 ≤ 12
Subtract 4 from both sides:
4x ≤ 8
Divide by 4:
x ≤ 2
So the solution for the first inequality is x ≤ 2.
To solve the second inequality:
5x - 7 < 7x + 3
Subtract 5x from both sides:
-7 < 2x + 3
Subtract 3 from both sides:
-10 < 2x
Divide by 2:
-5 < x
So the solution for the second inequality is x > -5.
Therefore, the solutions to the system of inequalities are -5 < x ≤ 2.