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Karen found that the solution to [tex]\(x - 7 + 5x = 36\)[/tex] is [tex]\(x = 6\)[/tex]. Which of these could be the way she found the solution?

A. Add [tex]\(x - 7 + 5x\)[/tex], add 36 to both sides of the equation.
B. Add [tex]\(x + 5x\)[/tex], subtract 7 from both sides of the equation.
C. Add [tex]\(x + 5x\)[/tex], add 7 to both sides of the equation.
D. Add [tex]\(-7\)[/tex] and [tex]\(5x\)[/tex], subtract [tex]\(x\)[/tex] from both sides of the equation.

Sagot :

GinnyAnswer
Let's start by examining the given equation step-by-step to find the correct way Karen could have found the solution.

The equation is:
[tex]\[ x - 7 + 5x = 36 \][/tex]

Step 1: Combine the like terms on the left side of the equation. The like terms here are [tex]\( x \)[/tex] and [tex]\( 5x \)[/tex]:

[tex]\[ (x + 5x) - 7 = 36 \][/tex]
[tex]\[ 6x - 7 = 36 \][/tex]

Step 2: To isolate the variable [tex]\( x \)[/tex], add 7 to both sides of the equation:

[tex]\[ 6x - 7 + 7 = 36 + 7 \][/tex]
[tex]\[ 6x = 43 \][/tex]

Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 6:
[tex]\[ x = \frac{43}{6} \][/tex]

Thus, the correct option is:
[tex]\[ \boxed{\text{Add } x + 5x, \text{add 7 to both sides of the equation.}} \][/tex]
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