Answers Algebra ISolving Linear Equations: Variables on Both Sides

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Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then decreases its speed, as time increases?

A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, is steady for a while, and then goes down over time.

A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins in the middle of the vertical axis, goes down at first, is steady for a while, and then goes up over time.

A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, goes down for a while, and then is steady over time.

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A graph titled Calories in Strawberries. The x-axis shows the number of strawberries, numbered 1 to 9, and the y-axis shows the number of calories, numbered 3 to 27. A straight line with a positive slope begins at point (0, 0) and ends at point (6.8, 27).

Each strawberry contains 4 calories.

Each strawberry contains 3 calories.

Twenty-four strawberries contain 6 calories.

Four strawberries contain 15 calories.

Eli left his house one afternoon to study at the library. The graph shows his distance, in miles, away from his house as a function of time, in minutes.

Eli arrived at the library.

Eli rode his bicycle home from the library.

Eli rode his bicycle to the store, getting farther away from his house.

Eli continued to study at the library for 13 more minutes.

What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12?

(–∞, –3]

[–3, ∞)

(–∞, 15]

[15, ∞)

What is the value of x in the equation 3x – y = 18, when y = 27?

Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. She spends of her paycheck on dinner with friends. If she had not earned the bonus, the amount she spent on dinner would have been of her paycheck. Which equation can be used to find h, the number of hours Lindsay worked last week?

(10h + 60) = (10h)

(10h + 60h) = (10h)

h(10 + 60) = h(10)

(10 + 60h) = (10h)

What is the value of p in the linear equation ?

−4

−2

Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lb. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?

3x – 10y = 50

3x = 50 – 10y

50 + 10y = 3y

50 + 3y = 10y

Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.What is the missing step of her solution?

Add 10.4 to both sides.

Add negative 10.4 to both sides.

Multiply both sides of the equation by 10.4.

Divide both sides of the equation by 10.4.

How many solutions exist for the given equation?3(x + 10) + 6 = 3(x + 12)

zero

one

two

infinitely many

Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?

(x + 30 + 60) = x

(x) = x(30 + 60)

x(30 + 60) = x

(x) = (30 + 60)

The axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.What is the equation when solved for a?

Option

Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?

6 + 2(x + 4) = (3 – x)

6 + 2(x + 4) = (x – 3)

(6 + 2)(x + 4) = (3 – x)

(6 + 2)(x + 4) = (x – 3)

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

v +4 = 8 – v

v +4 = 8

4 + v = 8 – v

2v + 4 = 8

Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute?

2 feet

12 feet

720 feet

7,200 feet

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