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How many solutions are there to the equation below?

7(x + 2) = 7x - 10

A. Infinitely many solutions
B. No solution
C. One solution

Sagot :

GinnyAnsweridn
Let's solve the equation step by step to determine the number of solutions:

The given equation is:
[tex]\[ 7(x + 2) = 7x - 10 \][/tex]

Step 1: Distribute the 7 on the left side.
[tex]\[ 7 \cdot (x + 2) = 7x - 10 \][/tex]
[tex]\[ 7x + 14 = 7x - 10 \][/tex]

Step 2: Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constant terms to the other side. Subtract [tex]\( 7x \)[/tex] from both sides.
[tex]\[ 7x + 14 - 7x = 7x - 10 - 7x \][/tex]
[tex]\[ 14 = -10 \][/tex]

Step 3: Assess the result.
[tex]\[ 14 = -10 \][/tex] is a contradiction. This indicates that the equation has no solution since 14 can never equal -10.

Thus, the correct answer is:

B. No solution
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