QuestionSolve the equations: 3q + 6 = q + 8 and 2q + 6 = 8. Find $2q=$ , $q=$ , and simplify fractions.

Studdy Solution

STEP 1

Assumptions1. We are given two equations $3q +6 = q +8$ and $q +6 =8$ . We are asked to solve for $q$ in both equations3. The operations of addition, subtraction, multiplication, and division are allowed in solving for $q$

STEP 2

Let's start with the first equation. We can simplify it by subtracting $q$ from both sides.
$q - q +6 = q - q +8$

STEP 3

Perform the subtraction on both sides to simplify the equation.
$2q +6 =8$

STEP 4

Now, let's solve the second equation. We can simplify it by subtracting6 from both sides.
$2q +6 -6 =8 -6$

STEP 5

Perform the subtraction on both sides to simplify the equation.
$2q =2$

STEP 6

To solve for $q$ , we can divide both sides of the equation by2.
$\frac{2q}{2} = \frac{2}{2}$

STEP 7

Perform the division on both sides to find the value of $q$ .
$q =1$ So, the solution to both equations is $q =1$ .

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QuestionSolve the equations: 3q + 6 = q + 8 and 2q + 6 = 8. Find $2q=$ , $q=$ , and simplify fractions.

Studdy Solution

STEP 1

Assumptions1. We are given two equations $3q +6 = q +8$ and $q +6 =8$ . We are asked to solve for $q$ in both equations3. The operations of addition, subtraction, multiplication, and division are allowed in solving for $q$

STEP 2

Let's start with the first equation. We can simplify it by subtracting $q$ from both sides.
$q - q +6 = q - q +8$

STEP 3

Perform the subtraction on both sides to simplify the equation.
$2q +6 =8$

STEP 4

Now, let's solve the second equation. We can simplify it by subtracting6 from both sides.
$2q +6 -6 =8 -6$

STEP 5

Perform the subtraction on both sides to simplify the equation.
$2q =2$

STEP 6

To solve for $q$ , we can divide both sides of the equation by2.
$\frac{2q}{2} = \frac{2}{2}$

STEP 7

Perform the division on both sides to find the value of $q$ .
$q =1$ So, the solution to both equations is $q =1$ .

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QuestionSolve the equations: 3q + 6 = q + 8 and 2q + 6 = 8. Find 2q=2q=2q=, q=q=q=, and simplify fractions.

Studdy Solution

STEP 1

Assumptions1. We are given two equations 3q+6=q+83q +6 = q +83q+6=q+8 and q+6=8q +6 =8q+6=8 . We are asked to solve for qqq in both equations3. The operations of addition, subtraction, multiplication, and division are allowed in solving for qqq

STEP 2

Let's start with the first equation. We can simplify it by subtracting qqq from both sides.q−q+6=q−q+8q - q +6 = q - q +8q−q+6=q−q+8

STEP 3

Perform the subtraction on both sides to simplify the equation.2q+6=82q +6 =82q+6=8

STEP 4

Now, let's solve the second equation. We can simplify it by subtracting6 from both sides.2q+6−6=8−62q +6 -6 =8 -62q+6−6=8−6

STEP 5

Perform the subtraction on both sides to simplify the equation.2q=22q =22q=2

STEP 6

To solve for qqq, we can divide both sides of the equation by2.2q2=22\frac{2q}{2} = \frac{2}{2}22q​=22​

STEP 7

Perform the division on both sides to find the value of qqq.q=1q =1q=1So, the solution to both equations is q=1q =1q=1.

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QuestionSolve the equations: 3q + 6 = q + 8 and 2q + 6 = 8. Find $2q=$ , $q=$ , and simplify fractions.

Assumptions1. We are given two equations $3q +6 = q +8$ and $q +6 =8$ . We are asked to solve for $q$ in both equations3. The operations of addition, subtraction, multiplication, and division are allowed in solving for $q$

Let's start with the first equation. We can simplify it by subtracting $q$ from both sides.
$q - q +6 = q - q +8$

Perform the subtraction on both sides to simplify the equation.
$2q +6 =8$

Now, let's solve the second equation. We can simplify it by subtracting6 from both sides.
$2q +6 -6 =8 -6$

Perform the subtraction on both sides to simplify the equation.
$2q =2$

To solve for $q$ , we can divide both sides of the equation by2.
$\frac{2q}{2} = \frac{2}{2}$

Perform the division on both sides to find the value of $q$ .
$q =1$ So, the solution to both equations is $q =1$ .