Math

QuestionDetermine the number of solutions for the equation: 12m+18=3(4m+6)-12 m + 18 = 3(-4 m + 6). Options: no solution, one solution, infinitely many solutions.

Studdy Solution

STEP 1

Assumptions1. The equation is given as 12m+18=3(4m+6)-12 m+18=3(-4 m+6). We are looking for the number of solutions to this equation

STEP 2

We need to simplify the equation. Start by distributing the on the right side of the equation.
12m+18=(4m+6)-12 m+18=(-4 m+6)12m+18=12m+18-12 m+18=-12 m+18

STEP 3

Now, let's subtract 12m-12m from both sides of the equation to isolate mm on one side.
12m+18(12m)=12m+18(12m)-12 m+18-(-12 m)=-12 m+18-(-12 m)18=1818=18

STEP 4

The equation 18=1818=18 is always true, regardless of the value of mm. This means that the original equation is true for all values of mm.
Therefore, the equation has infinitely many solutions.

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