Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Solve.

Separate your answers with a comma.

[tex]\[ |x-7|=4 \][/tex]

[tex]\[ \square \][/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\( |x - 7| = 4 \)[/tex], we need to consider the definition of absolute value. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, if [tex]\( |x - 7| = 4 \)[/tex], [tex]\( x - 7 \)[/tex] could be either 4 or -4.

We can break this down into two separate cases:

Case 1:
[tex]\[ x - 7 = 4 \][/tex]

To find [tex]\( x \)[/tex], solve for [tex]\( x \)[/tex]:
[tex]\[ x - 7 = 4 \][/tex]
[tex]\[ x = 4 + 7 \][/tex]
[tex]\[ x = 11 \][/tex]

Case 2:
[tex]\[ x - 7 = -4 \][/tex]

Again, solve for [tex]\( x \)[/tex]:
[tex]\[ x - 7 = -4 \][/tex]
[tex]\[ x = -4 + 7 \][/tex]
[tex]\[ x = 3 \][/tex]

Thus, the solutions to the equation [tex]\( |x - 7| = 4 \)[/tex] are:
[tex]\[ x = 11 \text{ or } x = 3 \][/tex]

So, the final answers are:
[tex]\[ 11, 3 \][/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.