Question

3x + (5x - 2) <3 - 2x, 1034. 1)4(5x - 1) - 21x > 1 - 3x;17-11x < 9x - 2(5x + 7),16- X > 2(1 - 4x) - 3(1 - 3x).​

Answer 1

$3x + (5x - 2) < 3 - 2x \\ 3x + 5x - 2 < 3 - 2x \\ 3x + 5x + 2x < 3 + 2 \\ 10x < 5 \\ x < 0.5$

$4(5x - 1) - 21x > 1 - 3x \\ 20x - 4 - 21x > 1 - 3x \\ 20x - 21x + 3x > 1 + 4\\ 2x > 5 \\ x > 2.5$

$17 - 11x < 9x - 2(5x + 7) \\ 17 - 11x < 9x - 10x - 14 \\ - 11x - 9x + 10x < - 14 - 17 \\ - 10x < - 31 \\ x > 3.1$

$16 - x > 2(1 - 4x) - 3(1 - 3x) \\ 16 - x > 2 - 8x - 3 + 9x \\ - x + 8x - 9x > 2 - 3 - 16 \\ - 2x > - 17 \\ x < 8.5$

Answer 2

Let's solve each inequality step-by-step:

1. $3x + (5x - 2) < 3 - 2x$

First, simplify the equation:

$3x + 5x - 2 < 3 - 2x$

Combine like terms:

$8x - 2 < 3 - 2x$

Add 2x to both sides to move all x terms to one side:

$8x + 2x - 2 < 3$

$10x - 2 < 3$

Add 2 to both sides to isolate the x term:

$10x < 5$

Now, divide both sides by 10 to solve for x:

$x < \frac{1}{2}$

So, the solution for this inequality is $x < \frac{1}{2}$.

2. $4(5x - 1) - 21x > 1 - 3x$

First, simplify the equation:

$20x - 4 - 21x > 1 - 3x$

Combine like terms:

$-x - 4 > 1 - 3x$

Add 3x to both sides to move all x terms to one side:

$-x + 3x - 4 > 1$

$2x - 4 > 1$

Add 4 to both sides to isolate the x term:

$2x > 5$

Now, divide both sides by 2 to solve for x:

$x > \frac{5}{2}$

So, the solution for this inequality is $x > \frac{5}{2}$.

3. $17 - 11x < 9x - 2(5x + 7)$

First, simplify the equation:

$17 - 11x < 9x - 10x - 14$

Combine like terms:

$17 - 11x < -x - 14$

Add x to both sides to move all x terms to one side:

$17 - 11x + x < -14$

$17 - 10x < -14$

Subtract 17 from both sides to isolate the x term:

$-10x < -31$

Now, divide both sides by -10. When dividing by a negative number, remember to flip the inequality sign:

$x > \frac{-31}{-10}$

$x > \frac{31}{10}$

So, the solution for this inequality is $x > \frac{31}{10}$.

4. $16 - x > 2(1 - 4x) - 3(1 - 3x)$

First, simplify the equation:

$16 - x > 2 - 8x - 3 + 9x$

Combine like terms:

$16 - x > 2 + x$

Subtract x from both sides to move all x terms to one side:

$16 - x - x > 2$

$16 - 2x > 2$

Subtract 16 from both sides to isolate the x term:

$-2x > -14$

Now, divide both sides by -2. When dividing by a negative number, remember to flip the inequality sign:

$x < \frac{-14}{-2}$

$x < 7$

So, the solution for this inequality is $x < 7$.

To summarize the solutions:

1. $x < \frac{1}{2}$

2. $x > \frac{5}{2}$

3. $x > \frac{31}{10}$

4. $x < 7$