ax - 4 < 12

Answer 1

To solve the inequality ax - 4 < 12, we need to isolate the variable 'x' on one side of the inequality sign.

First, add 4 to both sides of the inequality:

ax - 4 + 4 < 12 + 4

Simplifying, we get:

ax < 16

Next, to isolate 'x', divide both sides of the inequality by 'a':

(ax)/a < 16/a

This simplifies to:

x < 16/a

Therefore, the solution to the inequality ax - 4 < 12 is x < 16/a.

Answer 2

-4(4 + 7x) ≥ -7x + 5

Answer 3

To solve the inequality -4(4 + 7x) ≥ -7x + 5, we need to simplify both sides and isolate the variable 'x'.

Starting with the left side:

-4(4 + 7x) = -16 - 28x

Now, rewrite the inequality:

-16 - 28x ≥ -7x + 5

Next, simplify the right side:

-16 - 28x ≥ -7x + 5
-16 - 28x + 7x ≥ 5

Combine like terms:

-16 - 21x ≥ 5

Add 16 to both sides:

-21x ≥ 5 + 16
-21x ≥ 21

Now, divide both sides by -21. Since we are dividing by a negative number, the inequality sign flips:

x ≤ 21/-21
x ≤ -1

Therefore, the solution to the inequality -4(4 + 7x) ≥ -7x + 5 is x ≤ -1.

Answer 4

2(2x - 8) - 8x ≤ 0

Answer 5

To solve the inequality 2(2x - 8) - 8x ≤ 0, we need to simplify both sides and isolate the variable 'x'.

Starting with the left side:

2(2x - 8) - 8x = 4x - 16 - 8x = -4x - 16

Now, rewrite the inequality:

-4x - 16 ≤ 0

Next, add 16 to both sides:

-4x - 16 + 16 ≤ 0 + 16
-4x ≤ 16

Now, divide both sides by -4. Since we are dividing by a negative number, the inequality sign flips:

x ≥ 16/-4
x ≥ -4

Therefore, the solution to the inequality 2(2x - 8) - 8x ≤ 0 is x ≥ -4.

Answer 6

5x + (x - 8) > 9/2 (2x - 4)

Answer 7

To solve the inequality 5x + (x - 8) > 9/2 (2x - 4), we will simplify both sides and isolate the variable 'x'.

Starting with the right side:

9/2 (2x - 4) = 9x - 18

Now, rewrite the inequality:

5x + (x - 8) > 9x - 18

Next, distribute 9/2 to (2x - 4):

5x + x - 8 > 9x - 18

Combine like terms:

6x - 8 > 9x - 18

Now, subtract 6x from both sides:

-8 > 3x - 18

Next, add 18 to both sides:

-8 + 18 > 3x - 18 + 18

10 > 3x

Finally, divide both sides by 3:

10/3 > x

Therefore, the solution to the inequality 5x + (x - 8) > 9/2 (2x - 4) is x < 10/3.

Answer 8

Tom is deciding whether or not he should become a member of the gym to use their basketball courts. The membership cost is $125. Members pay $3 to rent out the basketball courts. How many times can Tom play basketball if he wants to spend no more than $200?

Answer 9

Let's assume Tom plays basketball 'x' times.

The cost of becoming a member is $125, and the cost to rent out the basketball courts each time is $3. Therefore, Tom's total cost can be calculated as:
125 + 3x

We want to find the maximum number of times Tom can play basketball with a budget of $200. So we set up the inequality:
125 + 3x ≤ 200

To solve this inequality, we need to isolate 'x'. First, subtract 125 from both sides:
3x ≤ 200 - 125
3x ≤ 75

Next, divide both sides by 3:
3x/3 ≤ 75/3
x ≤ 25

Therefore, Tom can play basketball no more than 25 times to stay within his budget of $200.