The problem to solve is:
6x+2(x+4)‹2x+20
First, let's work on the left hand side of your inequality, the 6x+2(x+4)
This means, for instance, to see if it can be simplified at all.
Multiply x and 6
Multiply x and 1
The x just gets copied along.
The answer is x
x
6*x evaluates to 6x
x+4 evaluates to x+4
Multiply 2 by x+4
we multiply 2 by each term in x+4 term by term.
This is the distributive property of multiplication.
Multiply 2 and x
Multiply 1 and x
The x just gets copied along.
x
2 × x = 2x
Multiply 2 and 4
1
2 × 4 = 8
2*(x+4) evaluates to 2x+8
6x + 2x = 8x
The answer is 8x+8
6*x+2*(x+4) evaluates to 8x+8
So, all-in-all, the left hand side of your inequality can be written as: 8x+8
Now, let's work on the right hand side of your inequality, the 2x+20
Multiply x and 2
Multiply x and 1
The x just gets copied along.
The answer is x
x
2*x evaluates to 2x
2*x+20 evaluates to 2x+20
The right hand side of your inequality can be written as: 2x+20
So with these (any) simplifications, the inequality we'll set out to solve is:
8x+8 ‹ 2x+20
Move the 8 to the right hand side by subtracting 8 from both sides, like this:
From the left hand side:
8 - 8 = 0
The answer is 8x
From the right hand side:
20 - 8 = 12
The answer is 12+2x
Now, the inequality reads:
8x ‹ 12+2x
Move the 2x to the left hand side by subtracting 2x from both sides, like this:
From the left hand side:
8x - 2x = 6x
The answer is 6x
From the right hand side:
2x - 2x = 0
The answer is 12
Now, the inequality reads:
6x ‹ 12
To isolate the x, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the x on the left side of the inequality.
The last step is to divide both sides of the inequality by 6 like this:
To divide x by 1
The x just gets copied along in the numerator.
The answer is x
6x ÷ 6 = x
12 ÷ 6 = 2
The solution to your inequality is:
x ‹ 2
So, your solution is:
x must be less than 2The problem to solve is:
6x+2(x+4)‹2x+20
First, let's work on the left hand side of your inequality, the 6x+2(x+4)
This means, for instance, to see if it can be simplified at all.
Multiply x and 6
Multiply x and 1
The x just gets copied along.
The answer is x
x
6*x evaluates to 6x
x+4 evaluates to x+4
Multiply 2 by x+4
we multiply 2 by each term in x+4 term by term.
This is the distributive property of multiplication.
Multiply 2 and x
Multiply 1 and x
The x just gets copied along.
x
2 × x = 2x
Multiply 2 and 4
1
2 × 4 = 8
2*(x+4) evaluates to 2x+8
6x + 2x = 8x
The answer is 8x+8
6*x+2*(x+4) evaluates to 8x+8
So, all-in-all, the left hand side of your inequality can be written as: 8x+8
Now, let's work on the right hand side of your inequality, the 2x+20
Multiply x and 2
Multiply x and 1
The x just gets copied along.
The answer is x
x
2*x evaluates to 2x
2*x+20 evaluates to 2x+20
The right hand side of your inequality can be written as: 2x+20
So with these (any) simplifications, the inequality we'll set out to solve is:
8x+8 ‹ 2x+20
Move the 8 to the right hand side by subtracting 8 from both sides, like this:
From the left hand side:
8 - 8 = 0
The answer is 8x
From the right hand side:
20 - 8 = 12
The answer is 12+2x
Now, the inequality reads:
8x ‹ 12+2x
Move the 2x to the left hand side by subtracting 2x from both sides, like this:
From the left hand side:
8x - 2x = 6x
The answer is 6x
From the right hand side:
2x - 2x = 0
The answer is 12
Now, the inequality reads:
6x ‹ 12
To isolate the x, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the x on the left side of the inequality.
The last step is to divide both sides of the inequality by 6 like this:
To divide x by 1
The x just gets copied along in the numerator.
The answer is x
6x ÷ 6 = x
12 ÷ 6 = 2
The solution to your inequality is:
x ‹ 2
So, your solution is:
x must be less than 2
and 
, the midpoint of the two endpoints 
is given by 
