Question

1)49-3(3-2z)≤1-4z 2)-0,5(8x+9)-0,9>4x-3 Решите неравенства.

Answer 1

Ответ:

Пошаговое объяснение:

1) 49 - 3(3-2z) $\leq$ 1 - 4z

  49 - 9 +6z $\leq$ 1 - 4z

   40 + 6z $\leq$ 1 - 4z

       10z $\leq$ -39

               z$\leq$ -3,9

2) -0,5(8x+9) - 0,9 > 4x - 3

     -4x - 4,5 - 0,9 > 4x - 3

           -8x > 2,4

              8x < -2,4

               x< -0,3

Answer 2

To solve these inequalities, we'll find the values of 'z' and 'x' that satisfy the given conditions. Let's solve each inequality step-by-step:

1. $49 - 3(3 - 2z) \leq 1 - 4z$

Step 1: Distribute the multiplication. $49 - 9 + 6z \leq 1 - 4z$

Step 2: Combine like terms. $40 + 6z \leq 1 - 4z$

Step 3: Move 'z' terms to one side and constants to the other side to isolate 'z'. Subtract 6z from both sides and add 1 to both sides: $40 + 6z + 4z \leq 1$ $10z + 40 \leq 1$

Step 4: Move the constant term to the other side. Subtract 40 from both sides: $10z \leq 1 - 40$ $10z \leq -39$

Step 5: Finally, divide by 10 to solve for 'z'. $z \leq \frac{-39}{10}$

So, the solution for the inequality is $z \leq -\frac{39}{10}$.

2. $-0.5(8x + 9) - 0.9 > 4x - 3$

Step 1: Distribute the multiplication. $-4x - 4.5 - 0.9 > 4x - 3$

Step 2: Combine like terms. $-4x - 5.4 > 4x - 3$

Step 3: Move 'x' terms to one side and constants to the other side to isolate 'x'. Add 4x to both sides and add 3 to both sides: $-4x - 4x > 3 + 5.4$ $-8x > 8.4$

Step 4: Divide by -8. Remember to reverse the inequality when dividing by a negative number. $x < \frac{8.4}{-8}$

Step 5: Finally, simplify the result. $x < -1.05$

So, the solution for the inequality is $x < -1.05$.

Answer 3

To solve the inequalities, we'll follow these steps:

1. Solve the first inequality: $49 - 3(3 - 2z) \leq 1 - 4z$
2. Solve the second inequality: $-0.5(8x + 9) - 0.9 > 4x - 3$

Let's start with the first inequality:

1. $49 - 3(3 - 2z) \leq 1 - 4z$

First, distribute the $3$ on the left side:

$49 - 9 + 6z \leq 1 - 4z$

Combine like terms:

$40 + 6z \leq 1 - 4z$

Next, move the variable terms ($6z$ and $-4z$) to one side of the inequality and the constant terms to the other side:

$6z + 4z \leq 1 - 40$

$10z \leq -39$

Now, divide by $10$, but remember to reverse the inequality since we're dividing by a negative number:

$z \geq -39/10$

So the solution to the first inequality is $z \geq -3.9$.

Now, let's move on to the second inequality:

2. $-0.5(8x + 9) - 0.9 > 4x - 3$

First, distribute the $-0.5$ on the left side:

$-4x - 4.5 - 0.9 > 4x - 3$

Combine like terms:

$-4x - 5.4 > 4x - 3$

Move the variable terms ($-4x$ and $4x$) to one side of the inequality and the constant terms to the other side:

$-4x - 4x > 3 - 5.4$

$-8x > -2.4$

Now, divide by $-8$, but remember to reverse the inequality since we're dividing by a negative number:

$x < -2.4/-8$

$x < 0.3$

So the solution to the second inequality is $x < 0.3$.

To summarize the solutions:

1. $z \geq -3.9$

2. $x < 0.3$