Question

1.9<4х+3<17 2.{2(x+6)-5x>=0 x/6-x/2<=1 3.{×/3-1/5 {x/4-1/3>x/6-3/4 Смотреть ответ kalmurzaevalaura kalmurzaevalaura 1) 9<4х+3<17 9<4х<17-3 9<4х<14 9х<14÷4 9х<3.5 х<3.5÷9 х<0.875

Answer 1

Let's solve the inequalities step by step:

1. $9 < 4x + 3 < 17$

To solve this inequality, we'll break it down into two separate inequalities:

a) $9 < 4x + 3$

Subtract 3 from both sides: $9 - 3 < 4x$ $6 < 4x$

Now, divide both sides by 4: $6/4 < x$ $1.5 < x$

b) $4x + 3 < 17$

Subtract 3 from both sides: $4x < 17 - 3$ $4x < 14$

Now, divide both sides by 4: $4x/4 < 14/4$ $x < 3.5$

So, the solution for the inequality $9 < 4x + 3 < 17$ is $1.5 < x < 3.5$.

2. $2(x+6) - 5x \geq 0$

First, simplify the left side: $2x + 12 - 5x \geq 0$

Combine like terms: $-3x + 12 \geq 0$

Now, isolate the variable: $-3x \geq -12$

Divide both sides by -3 (Note: When dividing or multiplying by a negative number, flip the inequality sign): $x \leq 4$

3. $\frac{x}{3} - \frac{1}{5} < \frac{x}{4} - \frac{1}{3}$

To compare fractions, we need to find a common denominator, which is 60:

Multiply both sides by 60 to get rid of the denominators: $60 \left( \frac{x}{3} - \frac{1}{5} \right) < 60 \left( \frac{x}{4} - \frac{1}{3} \right)$

Simplify: $20x - 12 < 15x - 20$

Now, isolate the variable: $20x - 15x < -20 + 12$ $5x < -8$

Finally, divide by 5: $x < -8/5$

So, the solution for the inequality $\frac{x}{3} - \frac{1}{5} < \frac{x}{4} - \frac{1}{3}$ is $x < -\frac{8}{5}$.

To summarize the solutions:

1. $1.5 < x < 3.5$
2. $x \leq 4$
3. $x < -\frac{8}{5}$