QuestionSolve the equation: $\frac{1}{3}(9 x+3)=3 x+1$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $\frac{1}{3}(9 x+3)=3 x+1$ . We are solving for the variable $x$

STEP 2

First, we need to simplify the equation. We can do this by distributing the $\frac{1}{}$ on the left side of the equation.
$\frac{1}{}(9 x+) = \frac{1}{}9x + \frac{1}{}$

STEP 3

Now, calculate the values for $\frac{1}{3}9x$ and $\frac{1}{3}3$ .
$\frac{1}{3}9x =3x$ $\frac{1}{3}3 =1$

STEP 4

Substitute these values back into the equation.
$3x +1 =3x +1$

STEP 5

Now, we can see that both sides of the equation are identical, which means that the equation is true for all real numbers $x$ .
Therefore, the solution to the equation $\frac{1}{3}(9 x+3)=3 x+1$ is all real numbers.

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QuestionSolve the equation: $\frac{1}{3}(9 x+3)=3 x+1$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $\frac{1}{3}(9 x+3)=3 x+1$ . We are solving for the variable $x$

STEP 2

First, we need to simplify the equation. We can do this by distributing the $\frac{1}{}$ on the left side of the equation.
$\frac{1}{}(9 x+) = \frac{1}{}9x + \frac{1}{}$

STEP 3

Now, calculate the values for $\frac{1}{3}9x$ and $\frac{1}{3}3$ .
$\frac{1}{3}9x =3x$ $\frac{1}{3}3 =1$

STEP 4

Substitute these values back into the equation.
$3x +1 =3x +1$

STEP 5

Now, we can see that both sides of the equation are identical, which means that the equation is true for all real numbers $x$ .
Therefore, the solution to the equation $\frac{1}{3}(9 x+3)=3 x+1$ is all real numbers.

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QuestionSolve the equation: 13(9x+3)=3x+1\frac{1}{3}(9 x+3)=3 x+131​(9x+3)=3x+1.

Studdy Solution

STEP 1

Assumptions1. The equation given is 13(9x+3)=3x+1\frac{1}{3}(9 x+3)=3 x+131​(9x+3)=3x+1 . We are solving for the variable xxx

STEP 2

First, we need to simplify the equation. We can do this by distributing the 1\frac{1}{}1​ on the left side of the equation.1(9x+)=1∗9x+1∗\frac{1}{}(9 x+) = \frac{1}{}*9x + \frac{1}{}*1​(9x+)=1​∗9x+1​∗

STEP 3

Now, calculate the values for 13∗9x\frac{1}{3}*9x31​∗9x and 13∗3\frac{1}{3}*331​∗3.13∗9x=3x\frac{1}{3}*9x =3x31​∗9x=3x13∗3=1\frac{1}{3}*3 =131​∗3=1

STEP 4

Substitute these values back into the equation.3x+1=3x+13x +1 =3x +13x+1=3x+1

STEP 5

Now, we can see that both sides of the equation are identical, which means that the equation is true for all real numbers xxx.Therefore, the solution to the equation 13(9x+3)=3x+1\frac{1}{3}(9 x+3)=3 x+131​(9x+3)=3x+1 is all real numbers.

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QuestionSolve the equation: $\frac{1}{3}(9 x+3)=3 x+1$ .

Assumptions1. The equation given is $\frac{1}{3}(9 x+3)=3 x+1$ . We are solving for the variable $x$

First, we need to simplify the equation. We can do this by distributing the $\frac{1}{}$ on the left side of the equation.
$\frac{1}{}(9 x+) = \frac{1}{}9x + \frac{1}{}$

Now, calculate the values for $\frac{1}{3}9x$ and $\frac{1}{3}3$ .
$\frac{1}{3}9x =3x$ $\frac{1}{3}3 =1$

Substitute these values back into the equation.
$3x +1 =3x +1$

Now, we can see that both sides of the equation are identical, which means that the equation is true for all real numbers $x$ .
Therefore, the solution to the equation $\frac{1}{3}(9 x+3)=3 x+1$ is all real numbers.