Question

use one-step equations to solve a variety of problems addition and subtraction are inverse operations. multiplication and division are inverse operations. inverse operations undo each other. use inverse operations to solve an equation. complementary angles are two angles whose measures have a sum of 90°. what is the value of x? a. write what you know. two angles form a right angle. one angle measures 53°. one angle measures x°. b. write an equation to represent the problem. 53 + x = 90 1. a room in the shape of a regular octagon has a perimeter of 72 feet. what is the length of each side of the room? let s represent the length in feet of each side of the room. write and solve an equation for s. 2. supplementary angles are two angles whose measures have a sum of 180°. what is the value of x? write and solve an equation for x. 3. maisie is watching a movie. she has been watching for 36 minutes. there are 55 minutes to go. how long does the movie last? let m represent the number of minutes that the movie lasts. write and solve an equation for m. 4. the area of a rectangle is found by using the formula a = l × w, where a is the area, l is the length, and w is the width. a rectangular desktop has an area of 18 square feet. the length of the desk is 6 feet. what is the width of the desktop? write and solve an equation for w. 5. sam has 36 pieces left to complete a puzzle. he has already put together 414 pieces. how many pieces p are in the puzzle? write and solve an equation for p.

Explanation:

Problem 1

Step1: Recall regular octagon sides

A regular octagon has 8 equal sides. Perimeter \( P = 8s \), where \( s \) is side length. Given \( P = 72 \), so equation: \( 8s = 72 \).

Step2: Solve for \( s \)

Divide both sides by 8: \( \frac{8s}{8} = \frac{72}{8} \) → \( s = 9 \).

Step1: Recall supplementary angles

Supplementary angles sum to \( 180^\circ \). One angle is \( 64^\circ \), other is \( x^\circ \). Equation: \( x + 64 = 180 \).

Step2: Solve for \( x \)

Subtract 64 from both sides: \( x = 180 - 64 \) → \( x = 116 \).

Step1: Define movie duration

Time watched + time remaining = total duration. Let \( m \) be total minutes. Equation: \( 36 + 55 = m \).

Step2: Calculate \( m \)

\( 36 + 55 = 91 \), so \( m = 91 \).

Answer:

Equation: \( 8s = 72 \), Solution: \( s = 9 \)

Problem 2