Certainly! Let's solve the system of inequalities step by step.
### Inequality 1:
[tex]\[ 4x + 7 > 4 - 2y \][/tex]
First, we want to isolate [tex]\( x \)[/tex] on one side of the inequality. To do this:
1. Subtract 4 from both sides:
[tex]\[ 4x + 7 - 4 > 4 - 4 - 2y \][/tex]
[tex]\[ 4x + 3 > -2y \][/tex]
2. To isolate [tex]\( x \)[/tex], divide every term by 4:
[tex]\[ x + \frac{3}{4} > -\frac{y}{2} \][/tex]
3. Subtract [tex]\(\frac{3}{4}\)[/tex] from both sides to further isolate [tex]\( x \)[/tex]:
[tex]\[ x > -\frac{y}{2} - \frac{3}{4} \][/tex]
So, the first inequality simplifies to:
[tex]\[ x > -\frac{y}{2} - \frac{3}{4} \][/tex]
### Inequality 2:
[tex]\[ 5y - 9 + 2x < -10 + 8x \][/tex]
First, we want to isolate [tex]\( y \)[/tex] on one side of the inequality. To do this:
1. Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ 5y - 9 < -10 + 8x - 2x \][/tex]
[tex]\[ 5y - 9 < -10 + 6x \][/tex]
2. Add 9 to both sides:
[tex]\[ 5y - 9 + 9 < -10 + 9 + 6x \][/tex]
[tex]\[ 5y < -1 + 6x \][/tex]
3. To isolate [tex]\( y \)[/tex], divide every term by 5:
[tex]\[ y < \frac{6x - 1}{5} \][/tex]
So, the second inequality simplifies to:
[tex]\[ y < \frac{6x}{5} - \frac{1}{5} \][/tex]
### Summary of Solutions:
1. From the first inequality:
[tex]\[ x > -\frac{y}{2} - \frac{3}{4} \][/tex]
2. From the second inequality:
[tex]\[ y < \frac{6x}{5} - \frac{1}{5} \][/tex]
These are the simplified forms of the given inequalities.
