what is 2x – 3 < 7 and 5 – x ≤ 8?

[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 Link

Аноним Аноним · Answer 2 · 2020-09-27T01:59:05+02:00

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)