6.10A Model Solve 1-Variable, 1-Step Eq/Inequalities (Part A)

Model & Solve

One-Variable & One-Step

Equations and Inequalities

(with Geometry)

6.10A

Model

• Diagrams

• Shapes

Solve

• Exact Answer

• Solution Set

Model & Solve

• Which inequality represents all possible values for x?

• What is the length/height of ...?

• What value for x makes this equation true?

Variable

• a letter that represents a number

• ex: x, t, b, r, h

One-Step

• Add or Subtract

• Multiply or Divide

One-Variable & One-Step

Equations

• expression with equal sign

Inequality/Inequalities

• greater than or less than

• greater than or equal to

• less than or equal to

Equations and Inequalities

How are greater than and less than similar?

​How are greater than or equal to similar to less than or equal to?

Multiple Choice

What value of x makes this equation true?

-80 = -110 + x

• -190

• -30

• 190

• 30

Multiple Choice

What value of x makes this equation true?

-110 = -80 + x

• -190

• -30

• 190

• 30

Multiple Select

The perimeter of a triangle is 144 units. One side length is 36 units. Which equations represent c, the combined length of the two other sides of the triangle?

Select TWO correct responses.

• c = 144 + 36

• c + 36 = 144

• 36 = c + 144

• 144 - 36 = c

• c - 36 = 144

Multiple Choice

The perimeter of a triangle is 144 units. One side length is 36 units. What is the combined length of the two other sides of the triangle?

• 108 units

• 112 units

• 0.25 units

• 180 units

Multiple Select

Benita will create a rectangle that has a height of 6 inches and an area of up to 84 square inches. Which TWO inequality represents all the possible lengths in units of the base, b, that Benita can use to create this rectangle?

• $$84\ \le6\cdot b$$

• $$84\ge6\cdot b$$

• $$84<6\cdot b$$

• $$84>6\cdot b$$

• $$b\le\frac{84}{6}$$

Multiple Select

Benita will create a rectangle that has a height of 6 inches and a maximum area of 84 square inches. Which inequality represents all the possible lengths in units of the base, b, that Benita can use to create this rectangle?

• $$b\le14$$

• $$b\ge14$$

• $$b\le78$$

• $$b\le90$$

Math Response

The area of a rectangle is 62.5 square inches. The base of the rectangle is 25 inches. What is the height of the rectangle in inches?

Type answer here

Correct Answer: 2.5

Deg^°

Rad

Multiple Choice

Dr. Benzon's car can travel no more than 510 miles on one full tank of gas. After filling up the tank with gas, she traveled 194 miles in the car.

The inequality that represents all possible values of m, the number of miles Dr. Benzon can travel in the car with the rest of the gas in the tank can be

$$510\ \ge\ m\ +\ 194$$

• True

• False

Multiple Choice

Dr. Benzon's car can travel a maximum of 510 miles on one full tank of gas. After filling up the tank with gas, she traveled 194 miles in the car.

Which inequality represents all possible values of m, the number of miles Dr. Benzon can travel in the car with the rest of the gas in the tank?

• $$m\ge704$$

• $$m\ge316$$

• $$m\le704$$

• $$m\le316$$

Dropdown

Dr. Benzon burns 256 calories rowing a boat each hour. She wants to burn more than 640 calories rowing a boat at the same rate.



What inequality represents all possible values for t, the number of hours Dr. Benzon must row a boat to burn more than 640 calories?

t ​

Select answer

​

Select answer

​

Multiple Choice

Dr. Benzon burns 256 calories rowing a boat each hour. She wants to exceed burning 640 calories rowing a boat at the same rate.

Which inequality represents all possible values for t, the number of hours Dr. Benzon must row a boat to burn more than 640 calories?

• 256 $$\cdot$$ t > 2.5

• 256 $$\cdot$$ t < 2.5

• t < 2.5 $$\cdot$$ 256

• t > 2.5 $$\cdot$$ 256