Answer:
[tex]x>-\frac{32}{9}[/tex]
Step-by-step explanation:
The given inequality is
[tex]-\frac{5}{2}(3x+4)<6-3x[/tex]
We need to solve this inequality to find the value of x.
Using distributive property we get
[tex]-\frac{5}{2}(3x)-\frac{5}{2}(4)<6-3x[/tex]
[tex]-\frac{15}{2}x-10<6-3x[/tex]
Add 3x on both sides.
[tex]-\frac{15}{2}x-10+3x<6-3x+3x[/tex]
[tex]\frac{-15x+6x}{2}-10<6[/tex]
Add 6 on both sides,
[tex]\frac{-9x}{2}<6+10[/tex]
[tex]\frac{-9x}{2}<16[/tex]
Multiply both sides by 2.
[tex]-9x<32[/tex]
Divide both sides by -9. The sign of inequality is changed if we multiply or divide the inequality by a negative number.
[tex]x>-\frac{32}{9}[/tex]
Therefore, the value of x is [tex]x>-\frac{32}{9}[/tex].
