First, understand the problem. Then translate the statement into an inequality.
the perimeter
of the rectangle
is less than or equal to
110
↓
↓
↓
x+35+
x plus 35
x+35
less than or equals
≤
110
Part 3
Simplify the left side of the inequality.
x+35+x+35
≤
110
2 x plus 70
2x+70
≤
110
(Simplify your answer. Do not factor.)
Part 4
Apply the addition property of inequality.
2x+70
≤
110
2x
≤
enter your response here
(Simplify your answer.)
2x + 70 ≤ 110
Subtract 70 from both sides:
2x ≤ 40
Divide both sides by 2:
x ≤ 20
First, understand the problem. Then translate the statement into an inequality.
the perimeter
of the rectangle
is less than or equal to
110
↓
↓
↓
x+35+
x plus 35
x+35
less than or equals
≤
110
Part 3
Simplify the left side of the inequality.
x+35+x+35
≤
110
2 x plus 70
2x+70
≤
110
(Simplify your answer. Do not factor.)
Part 4
Apply the addition property of inequality.
2x+70
≤
110
2x
≤
40
40
(Simplify your answer.)
Part 5
Next, apply the multiplication property of inequality,
2x
≤
40
x
≤
enter your response here
(Simplify your answer.)
2x ≤ 40
Divide both sides by 2:
x ≤ 20
First, understand the problem. Then translate the statement into an inequality.
the perimeter
of the rectangle
is less than or equal to
110
↓
↓
↓
x+35+
x plus 35
x+35
less than or equals
≤
110
Part 3
Simplify the left side of the inequality.
x+35+x+35
≤
110
2 x plus 70
2x+70
≤
110
(Simplify your answer. Do not factor.)
Part 4
Apply the addition property of inequality.
2x+70
≤
110
2x
≤
40
40
(Simplify your answer.)
Part 5
Next, apply the multiplication property of inequality,
2x
≤
40
x
≤
20
20
(Simplify your answer.)
Part 6
Finally, interpret the result.
The maximum width of a rectangle with a perimeter no greater than
110 centimeters and a length of
35 centimeters is
enter your response here
centimeters.
The maximum width of a rectangle with a perimeter no greater than 110 centimeters and a length of 35 centimeters is 20 centimeters.
To solve for x, we need to apply the addition property of inequality. Subtract 70 from both sides of the inequality:
2x + 70 ≤ 110
2x ≤ 110 - 70
2x ≤ 40
Now, divide both sides of the inequality by 2 to isolate x:
(2x)/2 ≤ 40/2
x ≤ 20
Therefore, the solution to the inequality is x ≤ 20.