Question

"Solve for Input of Function Given Output
Given } h(x)=-3 x-5 solve for x when } h(x)=-2 "

Answer 1

Answer: " x =
`-(7)/(3)` " ; or, write as: " x =
`-2(1)/(3)` " .

Explanation:

" Given h(x) = -3x − 5 ; solve for x when h(x) = 2 " .

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So, substitute 2 for h(x) ; and rewrite:
2 = -3x − 5 ;

Add 5 to Each Side of the equation;
2 + 5 = -3x − 5 + 5 ;

To get:

7 = -3x ;

Now divide Each Side of the equation by -3 ;

to isolate x on one side of the equation;

& to solve for x ;

7 / -3 = -3x / -3 ;
to get:
- 7/3 = x ;

↔ x = -
`(7)/(3)` ;

Or; to write as a mixed number:
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Note: -7/3 = - (7/3) = - (7 ÷ 3) ;

We can use long division to obtain the mixed number ;

→ which is the "opposite value of the following: " [7 ÷ 3]" ;

First: We shall solve for the value of [7 ÷ 3] ;
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2

3⟌ 7 ⇒ So we have " 2 R 1 " , or, "2 remainder 1" ;
- 6 ⇒ or: 2 and 1/3 ;
1
⇒ Note: The remainder; 1 , is the numerator ; and:
The divisor; 3, is the denominator ; and:

The number; 2, is the "whole number portion" of this mixed number.

[which we shall make, "- 2 "; as explained later.

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Second: We shall write out the mixed number" by:
A] writing the value from the information above' ; with our obtained values; as: "
`2(1)/(3)` " ; and by:

B] writing the correct 'mixed number' by writing the 'oppositive value'

of that said number. In our case, we take "
`2(1)/(3)` " ; and make the value "negative". In our case, we write the correct value by adding a
'negative sign'—as follows: "
`-2(1)/(3)` " .
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The answer is: " x =
`-(7)/(3)` " ; or, write as: " x =
`-2(1)/(3)` " .
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Hope this is helpful to you! Best wishes!
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