Answered

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If [tex][tex]$JM = 5x - 8$[/tex][/tex] and [tex][tex]$LM = 2x - 6$[/tex][/tex], which expression represents [tex][tex]$JL$[/tex][/tex]?

A. [tex][tex]$3x - 2$[/tex][/tex]
B. [tex][tex]$3x - 14$[/tex][/tex]
C. [tex][tex]$7x - 2$[/tex][/tex]
D. [tex][tex]$7x - 14$[/tex][/tex]

Sagot :

GinnyAnswer
Alright, let's solve the problem step-by-step.

We have two segments, [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex], which are parts of the line segment [tex]\( JL \)[/tex]. The given expressions are:
[tex]\[ JM = 5x - 8 \][/tex]
[tex]\[ LM = 2x - 6 \][/tex]

To find the expression for [tex]\( JL \)[/tex], we need to add the lengths of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex].

Combining [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex], we get:
[tex]\[ JL = JM + LM \][/tex]

Substitute the given expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[ JL = (5x - 8) + (2x - 6) \][/tex]

Now, let's combine the like terms. First, combine the terms containing [tex]\( x \)[/tex]:
[tex]\[ JL = 5x + 2x \][/tex]

Next, combine the constant terms:
[tex]\[ JL = -8 - 6 \][/tex]

So we have:
[tex]\[ JL = 7x - 14 \][/tex]

Therefore, the expression that represents [tex]\( JL \)[/tex] is:
[tex]\[ 7x - 14 \][/tex]

Among the given choices, the correct answer is:
[tex]\[ 7x - 14 \][/tex]

So, the final answer is:
[tex]\[ \boxed{7x - 14} \][/tex]
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