Question

7x-12>3x+6 5(x+3)>7(x+1)+4 5+|x|>9

Answer 1

$1)\; \; 7x-12>3x+6\\\\4x>18\; ,\; \; x>\frac{18}{4}\; ,\; \; \boxed {x>4,5}\\\\2)\; \; 5(x+3)>7(x+1)+4\\\\5x+15>7x+11\\\\4>2x\; ,\; \; 2x4\; \; \Rightarrow \; \; \left [ {{x>4} \atop {x$

Answer 2

Let's solve each inequality step by step:

1. 7x - 12 > 3x + 6

To solve this inequality, we need to isolate the variable x on one side of the inequality sign. First, we can move all the x terms to one side by subtracting 3x from both sides:

7x - 3x - 12 > 3x - 3x + 6

Simplify:

4x - 12 > 6

Next, we can move the constant term (-12) to the other side by adding 12 to both sides:

4x - 12 + 12 > 6 + 12

Simplify:

4x > 18

Finally, to isolate x, we divide both sides by 4:

4x/4 > 18/4

Simplify:

x > 4.5

So, the solution to the inequality is x > 4.5.

2. 5(x + 3) > 7(x + 1) + 4

Let's start by expanding the terms on both sides of the inequality:

5x + 15 > 7x + 7 + 4

Simplify:

5x + 15 > 7x + 11

Now, let's move all the x terms to one side by subtracting 5x from both sides:

5x - 5x + 15 > 7x - 5x + 11

Simplify:

15 > 2x + 11

Next, let's move the constant term (11) to the other side by subtracting 11 from both sides:

15 - 11 > 2x + 11 - 11

Simplify:

4 > 2x

Finally, isolate x by dividing both sides by 2:

4/2 > 2x/2

Simplify:

2 > x

So, the solution to the inequality is x < 2.

3. 5 + |x| > 9

To solve this inequality, we need to consider the two cases when x is positive and when x is negative, due to the absolute value.

Case 1: x is positive (x > 0)

In this case, the absolute value of x is just x itself:

5 + x > 9

Subtract 5 from both sides:

5 + x - 5 > 9 - 5

Simplify:

x > 4

Case 2: x is negative (x < 0)

In this case, the absolute value of x is -x:

5 - x > 9

Subtract 5 from both sides:

5 - x - 5 > 9 - 5

Simplify:

-x > 4

To solve for x, we need to multiply both sides by -1, but we also need to reverse the inequality direction when multiplying or dividing by a negative number:

-x * (-1) < 4 * (-1)

Simplify:

x < -4

So, the solutions to the inequality are x > 4 or x < -4.

In summary:

1. x > 4.5
2. x < 2
3. x > 4 or x < -4