Answers NJ-Algebra I CRSolving Linear Equations: Variables on Both Sides

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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.

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

zero

one

two

infinitely many

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)

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)

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

The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the gravitational constant, g. This can be modeled by the equation P = mgh.

= h

Pmg = h

= h

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)

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

x = 6

x = 7

x = 8

x = 9

A graph titled Cost of Erasers. The x-axis shows the number of erasers, numbered 1 to 9, and the y-axis shows the total cost in dollars, numbered 0.5 to 4.5. Blue diamonds appear at points (1, 0.5), (2, 1), (3, 1.5), (4, 2), (5, 2.5), (6, 3), (7, 3.5), (8, 4), (9, 4.5).

Each eraser costs $1.00.

Each eraser costs $1.50.

Three erasers cost $6.

Seven erasers cost $3.50.

A family uses 12,986.64 Swiss francs per year to pay a mortgage that requires US dollars. Approximately how much, in US dollars, does the family spend per month on the mortgage?1 US dollar = 0.9019 Swiss francs1 Swiss franc = 1.11 US dollar

$975

$1,080

$1,200

$1,440

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

(–∞, –3]

[–3, ∞)

(–∞, 15]

[15, ∞)

A frozen yogurt shop offers a rewards system for frequent customers. The graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased.

A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.

A rewards customer pays $5 per ounce because the total amount paid is always increasing.

A rewards customer pays $20 for 10 or 12 ounces of yogurt because the total amount paid is increasing.

A rewards customer earns 5 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s=180(n−2), where n is the number of sides.Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°? Round to the nearest whole number.

6 sides

7 sides

8 sides

9 sides

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

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