Linear Equations in Real-World Scenarios Quick Check
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Question
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)
Responses
a+2=3(a−6+2)
a plus 2 equals 3 left parenthesis a minus 6 plus 2 right parenthesis
a=3(a+2)
a equals 3 left parenthesis a plus 2 right parenthesis
a+2=3(a+6+2)
a plus 2 equals 3 left parenthesis a plus 6 plus 2 right parenthesis
3(a+2)=a−6+2
3 left parenthesis a plus 2 right parenthesis equals a minus 6 plus 2
The correct answer is: a+2=3(a−6+2)
Simplify: −4(2x+5)
(1 point)
Responses
(−4×2x)+(−4×5)
open paren negative 4 times 2 x close paren plus open paren negative 4 times 5 close paren
(−4−2x)+(−4−5)
open paren negative 4 minus 2 x close paren plus open paren negative 4 minus 5 close paren
(−4+2x)×(−4+5)
open paren negative 4 plus 2 x close paren times open paren negative 4 plus 5 close paren
(−4÷2x)+(−4÷5)
The correct answer is: (−4×2x)+(−4×5)
explain
To simplify the expression −4(2x+5), you need to multiply −4 by each term inside the parentheses.
Starting with the expression 2x+5 inside the parentheses, you distribute the −4 to each term:
−4(2x+5) = −4(2x) + (-4)(5)
This simplifies to:
−8x + (-20)
So the simplified expression is −8x - 20.
A student solves the following problem: 2(x - 2) + 5x = 24
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
(1 point)
Responses
Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
Step 1: The student should have only distributed the 2 and x, not the x & -2.
Step 1: The student should have only distributed the 2 and x, not the x & -2.
Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
Step 3: The student should have subtracted 4 from both sides, not added 4.
The mistake the student made is in Step 3. They should have subtracted 4 from both sides of the equation, not added 4.
The correct Step 3 should be:
10x - 4 - 4 = 24 - 4
This simplifies to:
10x - 8 = 20