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Sagot :
We are given the following equation
[tex]-3\mleft(x-14\mright)+9x=6x+42[/tex]Let us solve the equation for x.
Step 1:
Multiply the term -3 with the terms in the parenthesis.
[tex]\begin{gathered} -3(x-14)+9x=6x+42 \\ -3x+42+9x=6x+42 \end{gathered}[/tex]Step 2:
Simplify the terms on the left-hand side of the equation
[tex]\begin{gathered} -3x+42+9x=6x+42 \\ 42+6x=6x+42 \end{gathered}[/tex]Step 3:
Combine the like terms together.
[tex]\begin{gathered} 42+6x=6x+42 \\ 42-42=6x-6x \\ 0=0 \end{gathered}[/tex]This means that this equation has an infinite number of possible solutions.
If you notice the left and right side of the equation are exactly the same.
[tex]42+6x=6x+42[/tex]This means that whatever value of x you put into this equation, the equation will always be satisfied.
Try substituting some values for x.
[tex]\begin{gathered} 42+6(1)=6(1)+42 \\ 42+6=6+42 \\ 48=48 \end{gathered}[/tex][tex]\begin{gathered} 42+6(-2)=6(-2)+42 \\ 42-12=-12+42 \\ 30=30 \end{gathered}[/tex]Hence, the given equation has an infinite number of possible solutions.
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