Answer:
[tex]\begin{bmatrix}x<5\\ x\ge \:-3\end{bmatrix}[/tex]
Step-by-step explanation:
[tex]2x -3 < 7 \\ 5 - x \leq 8\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:2x-3<7:\quad x<5\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:5-x\le \:8:\quad x\ge \:-3\\\\=\begin{bmatrix}x<5\\ x\ge \:-3\end{bmatrix}\\[/tex]
Answer:
Result for Inequality expression 1:
[tex]x < 5[/tex]
Result for Inequality expression 2:
[tex]x \geq -3[/tex]
Step-by-step explanation:
-Inequality expression 1:
[tex]2x - 3 < 7[/tex]
-Inequality expression 2:
[tex]5 - x \leq 8[/tex]
-Solve inequality expression 1:
[tex]2x - 3 < 7[/tex]
[tex]2x - 3 + 3 < 7 + 3[/tex]
[tex]2x < 10[/tex]
[tex]\frac{2x}{2} < \frac{10}{2}[/tex]
[tex]\boxed {x < 5}[/tex]
-Solve inequality expression 2:
[tex]5 - x \leq 8[/tex]
[tex]5 - 5 - x \leq 8 - 5[/tex]
[tex]- x \leq 3[/tex]
[tex]\frac{-x}{-1} \leq \frac{3}{-1}[/tex]
[tex]\boxed {x \geq -3}[/tex] (inequality sin changed by divide by a negative integer or variable)
