Question

Решить неравенства. a)2(3-x)-(4x-1)b)4(2a-1)-3(a+6)>ag)0,8(2-x)-0,6(3-2x)<4d)0,5(6-x)+(1+3x)>0,2e)0,6(2x+1)-0,4(3x+2)>1

Answer 1

b)

$4(2a - 1) - 3(a + 6) > a \\ 8a - 4 - 3a - 18 > a \\ 5a - 22 > a \\ 5a - a > 22 \\ 4a > 22 \\ a > \frac{11}{2}$

$0.8(2 - x) - 0.6(3 - 2x) < 4 \\ 1.6 - 0.8x - 1.8 + 1.2x < 4 \\ - 0.2 + 0.4x < 4 \\ 0.4x < 4 + 0.2 \\ 0.4x < 4.2 \\ x < 10.5$

$0.5(6 - x) + (1 + 3x) > 0.2 \\ 3 - 0.5x + 1 + 3x > 0.2 \\ 4 + 2.5x > 0.2 \\ 2.5x > 0.2 - 4 \\ 2.5x > - 3.8 \\ x > - 1.52$

$0.6(2x + 1) - 0.4(3x + 2) > 1 \\ 1.2x + 0.6 - 1.2x - 0.8 > 1 \\ - 0.2 > 1$не має коренів

Answer 2

Объяснение:

Решение представлено на фото

Answer 3

To solve each inequality, we'll go through them one by one:

a) $2(3-x) - (4x-1)$

Step 1: Distribute the terms inside the parentheses.

$6 - 2x - 4x + 1$

Step 2: Combine like terms.

$7 - 6x$

Now we have the inequality: $7 - 6x > 0$

Step 3: Solve for $x$:

$6x < 7$

$x < \frac{7}{6}$

b) $4(2a-1) - 3(a+6) > a$

Step 1: Distribute the terms inside the parentheses.

$8a - 4 - 3a - 18 > a$

Step 2: Combine like terms.

$8a - 3a - 4 - 18 > a$

$5a - 22 > a$

Step 3: Move all terms containing $a$ to one side and constants to the other side.

$5a - a > 22$

$4a > 22$

Step 4: Solve for $a$:

$a > \frac{22}{4}$

$a > \frac{11}{2}$

c) $0.8(2-x) - 0.6(3-2x) < 4$

Step 1: Distribute the terms inside the parentheses.

$1.6 - 0.8x - 1.8 + 1.2x < 4$

Step 2: Combine like terms.

$-0.8x + 1.2x - 0.2 < 4$

$0.4x - 0.2 < 4$

Step 3: Move constants to the other side.

$0.4x < 4.2$

Step 4: Solve for $x$:

$x < \frac{4.2}{0.4}$

$x < 10.5$

d) $0.5(6-x) + (1+3x) > 0.2$

Step 1: Distribute the terms inside the parentheses.

$3 - 0.5x + 1 + 3x > 0.2$

Step 2: Combine like terms.

$4 + 2.5x > 0.2$

Step 3: Move constants to the other side.

$2.5x > -3.8$

Step 4: Solve for $x$:

$x > \frac{-3.8}{2.5}$

$x > -1.52$

e) $0.6(2x+1) - 0.4(3x+2) > 1$

Step 1: Distribute the terms inside the parentheses.

$1.2x + 0.6 - 1.2x - 0.8 > 1$

Step 2: Combine like terms.

$0.6 - 0.8 > 1$

Step 3: Move constants to the other side.

$-0.2 > 1$

Since the above statement is not true, there is no valid solution for this inequality.

Final results for the inequalities:

a) $x < \frac{7}{6}$

b) $a > \frac{11}{2}$

c) $x < 10.5$

d) $x > -1.52$

e) No valid solution.