Literal Equations Answers

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A student solves the equation using the steps in the table. Original equationCross multiplicationDistributive propertySubtraction property of equality5 = xWhich method of solving for the variable could be used instead of cross multiplication?

Question illustration
A
distributing x + 3 and then 3x + 5 to both sides of the equation
B
distributing x – 3 and then 3x – 5 to both sides of the equation
C
using the multiplication property of equality to multiply both sides of the equation by 10
D
using the multiplication property of equality to multiply both sides of the equation by
Option D
2
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The selling price, s, of an item is s = c + mc, where c is the cost of the item and m is the percent markup based on cost. What is the formula solved for m?

A
m = StartFraction s minus c Over c EndFraction
Option A
B
m = StartFraction s + c Over c EndFraction
Option B
C
s minus c = m
Option C
D
s + c = m
Option D
3

Which equation is equivalent to

Question illustration
A
s = t minus 2
Option A
B
s = StartFraction 4 Over t + 2 EndFraction
Option B
C
s = StartFraction t + 2 Over 4 EndFraction
Option C
D
s = t + 6
Option D
4

When is solved for c, one equation is Which of the following is an equivalent equation to find c?

Question illustration
A
c = 10 b minus 10 minus 5
Option A
B
c = (10 b minus 10 minus 5) squared
Option B
C
c = StartFraction (10 b minus 2) squared Over 25 EndFraction
Option C
D
c = StartFraction (10b minus 10) squared Over 25 EndFraction
Option D
5

The formula for the nth term of an arithmetic sequence can be found using the formula . Which of the following is equivalent to this equation?

Question illustration
A
n = a Subscript n Baseline + a Subscript 1
Option A
B
n = StartFraction a Subscript n Baseline + a Subscript 1 Baseline minus 3 Over d EndFraction
Option B
C
n = a Subscript n Baseline minus a Subscript 1
Option C
D
n = a Subscript n Baseline minus a Subscript 1 Baseline + d Over d EndFraction
Option D
6

The equation is the slope-intercept form of the equation of a line. What is the equation solved for b?

Question illustration
A
y minus m = b
Option A
B
y minus m x = b
Option B
C
StartFraction y Over m x EndFraction = b
Option C
D
StartFraction y Over m EndFraction minus x = b
Option D
7

The area of a sector of a circle is given by the equation , where r is the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write?

Question illustration
A
360 uppercase A + pi r squared
Option A
B
360 uppercase A minus pi r squared
Option B
C
StartFraction 360 + uppercase A Over pi r squared EndFraction
Option C
D
StartFraction 360 uppercase A Over pi r squared EndFraction
Option D
8

Gavin wrote the equation to represent p, the profit he makes from s sales in his lawn-mowing business. Which equation is solved for s?

Question illustration
A
s = StartFraction p minus 100 Over 3 EndFraction
Option A
B
s = StartFraction 4 p minus 300 Over 3 EndFraction
Option B
C
s = StartFraction 4 p Over 300 EndFraction
Option C
D
s = StartFraction 400 p Over 3 EndFraction
Option D
9

Which of the following equations is equivalent to ?

Question illustration
A
h = uppercase S minus pi r squared
Option A
B
h = StartFraction uppercase S Over pi r squared EndFraction
Option B
C
h = StartFraction pi r squared Over uppercase S EndFraction
Option C
D
h = uppercase S + pi r squared
Option D
10

Remmi wrote the equation of the line He solved for x and got Which of the following is an equivalent equation for x?

Question illustration
A
x = y minus eleven-thirds
Option A
B
x = y + seven-thirds
Option B
C
x = 3 (y minus two-thirds)
Option C
D
x = 3 (y + two-thirds)
Option D

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