Question

the perimeter of a rectangle is to be no greater than 130 cm and one - side is to be 35 centimeters. find the maximum width of the rectangle.
x + 35 + x + 35 ≤ 130
simplify the left side of the inequality.
x + 35 + x + 35 ≤ 130
2x + 70 ≤ 130
(simplify your answer. do not factor.)
apply the addition property of inequality.
2x + 70 ≤ 130
2x ≤
(simplify your answer.)

Explanation:

Step1: Recall perimeter formula

Let the width be $x$ and length be 35. Perimeter $P = 2(x + 35)=x + 35+x + 35$, and $P\leq130$, so $x + 35+x + 35\leq130$.

Step2: Simplify left - hand side

Combine like terms: $x+x+35 + 35=2x+70$, so $2x + 70\leq130$.

Step3: Apply subtraction property of inequality

Subtract 70 from both sides: $2x+70 - 70\leq130 - 70$, which gives $2x\leq60$.

Step4: Apply division property of inequality

Divide both sides by 2: $\frac{2x}{2}\leq\frac{60}{2}$, so $x\leq30$.

Answer:

30 centimeters