2 Answers

Sam Dozor · Answer 1 · 2022-08-18T06:18:07+0000

Answer:

Equation:
$\large\sf\:(x\:-\:5)/(2)\:=\:-2$

Explanation:

Given the expression, "Half the difference of a number and 5 is -2" can be represented algebraically.

In order to make it easier to understand what the equation represents the given sentence, we must break it down into smaller portions.

Let x = a number.

In the phrase, "... difference of a number and 5" is the same as: x - 5.

Finally, given the phrase, "Half the difference of a number and 5 is -2" is the same as:
$\large\sf{(1)/(2)\:of\:x\:-\:5\:=-2}\\$ .

However, it is more appropriate to express the given statement in the following equation:

$\large\sf\:(x\:-\:5)/(2)\:=\:-2$ ⇒ This is the equation that represents the given statement.

If we actually solve for x, what we could do is to first multiply both sides by 2 in order to eliminate the fraction on the left-hand side:

$\large\sf\:(x\:-\:5)/(2)(2)\:=\:-2(2)$

x - 5 = -4

Finally, add 5 to both sides to solve for x:

x - 5 + 5 = -4 + 5

x = 1

Substituting the value of x into the equation:

$\large\sf\:(x\:-\:5)/(2)\:=\:-2$

$\large\sf\:(1\:-\:5)/(2)\:=\:-2$

$\large\sf\:(-4)/(2)\:=\:-2$

-2 = -2 (True statement). Therefore, we have the correct value for x.

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