1. ax - 4 < 12
To solve for x, we need to isolate the variable on one side of the inequality. Let's start by adding 4 to both sides:
ax - 4 + 4 < 12 + 4
This simplifies to:
ax < 16
Next, divide both sides of the inequality by a:
(ax)/a < 16/a
x < 16/a
The solution is x < 16/a.
To graph this solution on a number line, we will use an open circle to represent the solution and shade the line to the left of the circle to indicate that x is less than the value.
2. -4(4 + 7x) ≥ -7x + 5
Start by simplifying the left side:
-4(4 + 7x) = -16 - 28x
The inequality becomes:
-16 - 28x ≥ -7x + 5
To solve for x, let's first bring all terms with x to one side of the inequality:
-16 - 28x + 7x ≥ 5
Combine like terms:
-16 - 21x ≥ 5
Now, let's isolate x by adding 16 to both sides:
-16 + 16 - 21x ≥ 5 + 16
Simplifying further:
-21x ≥ 21
Divide both sides by -21 (remember to flip the inequality when dividing by a negative number):
x ≤ -1
The solution is x ≤ -1.
To graph this solution on a number line, we will use a closed circle to represent the solution and shade the line to the left of the circle to indicate that x is less than or equal to the value.
3. 2(2x - 8) - 8x ≤ 0
Start by simplifying the left side:
2(2x - 8) - 8x = 4x - 16 - 8x = -4x - 16
The inequality becomes:
-4x - 16 ≤ 0
To solve for x, let's first add 16 to both sides:
-4x - 16 + 16 ≤ 0 + 16
Simplifying further:
-4x ≤ 16
Next, divide both sides by -4 (remember to flip the inequality when dividing by a negative number):
x ≥ -4
The solution is x ≥ -4.
To graph this solution on a number line, we will use a closed circle to represent the solution and shade the line to the right of the circle to indicate that x is greater than or equal to the value.
4. 5x + (x - 8) > (9/2)(2x - 4)
Start by simplifying the left side:
5x + x - 8 > 9x - 18
Combine like terms:
6x - 8 > 9x - 18
To solve for x, let's first subtract 6x and add 18 to both sides:
6x - 8 - 6x + 18 > 9x - 18 - 6x + 18
Simplifying further:
10 > 3x
Now, divide both sides by 3:
10/3 > x
The solution is x < 10/3.
To graph this solution on a number line, we will use an open circle to represent the solution and shade the line to the left of the circle to indicate that x is less than the value.
5. 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?
Let's set up an inequality to represent this situation:
125 + 3x ≤ 200
To solve for x, let's first subtract 125 from both sides:
125 - 125 + 3x ≤ 200 - 125
Simplifying further:
3x ≤ 75
Next, divide both sides by 3:
x ≤ 75/3
Simplifying further:
x ≤ 25
Tom can play basketball no more than 25 times if he wants to spend no more than $200.
8th grade Math Lesson 2-8 Practice
Problems: Show All Work: Solve and graph the solution on a number line.
1.ax - 4 < 12
2.-4(4 + 7x) ≥ -7x + 5
3.2(2x - 8) - 8x ≤ 0
4.5x + (x - 8) > 9/2 (2x - 4)
5.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?
1 answer