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ACT Exam  >  ACT Questions  >  Let x = 2y + 3z - 5. What happens to the valu... Start Learning for Free
Let x = 2y + 3z - 5. What happens to the value of x if the value of y decreases by 1 and the value of z increases by 2?
  • a)
    It decreases by 2
  • b)
    It is unchanged
  • c)
    It increases by 1
  • d)
    It increases by 2
  • e)
    It increases by 4
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
Let x = 2y + 3z - 5. What happens to the value of x if the value of y ...
Question Analysis:
We are given the equation x = 2y + 3z - 5 and we need to determine what happens to the value of x if the value of y decreases by 1 and the value of z increases by 2.

Given:
x = 2y + 3z - 5

Solution:
To find out what happens to the value of x, we need to substitute the new values of y and z into the equation and compare the result to the original value of x.

Step 1: Original value of x
We are given the equation x = 2y + 3z - 5. Let's substitute the original values of y and z into the equation to find the original value of x.

x = 2y + 3z - 5
x = 2(0) + 3(0) - 5 (Assuming y = 0 and z = 0 for simplicity)
x = 0 + 0 - 5
x = -5

So, the original value of x is -5.

Step 2: New values of y and z
According to the question, the value of y decreases by 1 and the value of z increases by 2. Let's substitute these new values into the equation to find the new value of x.

New value of y = y - 1
New value of z = z + 2

x = 2(y - 1) + 3(z + 2) - 5

Step 3: Simplify the equation
x = 2y - 2 + 3z + 6 - 5
x = 2y + 3z - 1

Comparing this equation with the original equation, we can see that the new value of x is 1 less than the original value of x.

So, the value of x decreases by 1 if the value of y decreases by 1 and the value of z increases by 2.

Therefore, the correct answer is option 'C'. The value of x increases by 1.
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Community Answer
Let x = 2y + 3z - 5. What happens to the value of x if the value of y ...
You are given that x = 2y + 3z − 5. If the value of y decreases by 1, then the new value of y is y − 1; if the value of z increases by 2, then the new value of z is z + 2.
Substitute these values into the original equation to see the effects of the changes on the value of x:
x = 2(y − 1) + 3(z + 2) − 5
x = 2y − 2 + 3z + 6 − 5 = 2y + 3z − 1
Therefore, x now equals 2y + 3z − 1, which is 4 more than 2y + 3z − 5.
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Let x = 2y + 3z - 5. What happens to the value of x if the value of y decreases by 1 and the value of z increases by 2?a)It decreases by 2b)It is unchangedc)It increases by 1d)It increases by 2e)It increases by 4Correct answer is option 'E'. Can you explain this answer?
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