Solve equation -2 • 4/5 = -3 1/2 • n

1 answer:

8 0

16/155 = n

explanation

A linear equation is an equation of a straight line. To solve linear equations, it is important to keep the following key concepts in mind:

Maintain balance of the equation by applying the same operations to both sides of an equation

Isolate for the variable by collecting like terms

Use inverse operations to rearrange an equation

to show your work

-8/ 5 = -31/2 • n
- 8/5 = -31n/2
2(-8/5) = 2 • -31/n
-16/5 = -31n
-16/5 / -31 = -31n/31
16/155 = n

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When you reverse the digits in a certain two-digit number you decrease its value by 18. what is the number if the sum of its dig

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Answer: The number is 75

Lets start by defining the 2-digit number.

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Define the number
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Let x be the digit in the tens place and y be the digit in the ones place.
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The reverse of the number is 10y + x

Now we will construct the equations needed

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Construct equations
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When the digits are reversed, the value decreases by 18:
(10x + y) - (10y + x) = 18 .   ← Apply distributive property
10x + y - 10y - x = 18   ←Combine like terms
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Now that we have the two equations, we can solve for x and y.

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Solve for x and y
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x - y = 2    ---------------------- (equation 1)
x + y = 12     ---------------------- (equation 2)

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Make x the subject in equation 1
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x - y = 2 ← Add y from both sides
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x = 2 + y

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Substitute x = 2 + y into equation 2
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x + y = 12   ← Substitute x = 2 + y
2 + y + y = 12 ← combine like terms
2 + 2y = 12    ← Subtract 2 from both sides
-2    -2
2y = 10       ← Divide by 2 on both sides
÷2 ÷2
y = 5

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Substitute y = 5 into equation 1
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x - y = 2   ← substitute y = 5
x - 5 = 2   ← add 5 on both sides
+5 +5
x = 7

Now we know the value of x and y. Lets find the 2-digit number.

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Find the 2-digit number
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The number = 10x + y = 10(7) + 5 = 75

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Answer: The number is 75
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