Solved on Jan 12, 2024

Solve the linear system and find the value of $q$ .

STEP 1

Assumptions
1. We are given an equation that needs to be simplified and solved for the variable $q$ .
2. The operations allowed are addition, subtraction, multiplication, and division.
3. We will follow the order of operations and properties of equality to solve the equation.

STEP 2

First, we need to simplify the left side of the equation by combining like terms.
$-9q + 8q = -1q$

STEP 3

Now, rewrite the equation with the simplified left side.
$-1q - 14 = 2q + 10$

STEP 4

Next, we want to isolate the variable $q$ on one side of the equation. To do this, we will subtract $2q$ from both sides of the equation to move all the $q$ terms to the left side.
$-1q - 2q - 14 = 2q - 2q + 10$

STEP 5

Simplify both sides of the equation after the subtraction.
$-3q - 14 = 10$

STEP 6

Next, we want to isolate the term with $q$ by getting rid of the constant on the left side. We will add $14$ to both sides of the equation.
$-3q - 14 + 14 = 10 + 14$

STEP 7

Simplify both sides of the equation after the addition.
$-3q = 24$

STEP 8

Now, to solve for $q$ , we will divide both sides of the equation by $-3$ .
$\frac{-3q}{-3} = \frac{24}{-3}$

STEP 9

Simplify both sides of the equation after the division.
$q = -8$
The solution to the equation is $q = -8$ .

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Solve the linear system and find the value of $q$ .

STEP 1

Assumptions
1. We are given an equation that needs to be simplified and solved for the variable $q$ .
2. The operations allowed are addition, subtraction, multiplication, and division.
3. We will follow the order of operations and properties of equality to solve the equation.

STEP 2

First, we need to simplify the left side of the equation by combining like terms.
$-9q + 8q = -1q$

STEP 3

Now, rewrite the equation with the simplified left side.
$-1q - 14 = 2q + 10$

STEP 4

Next, we want to isolate the variable $q$ on one side of the equation. To do this, we will subtract $2q$ from both sides of the equation to move all the $q$ terms to the left side.
$-1q - 2q - 14 = 2q - 2q + 10$

STEP 5

Simplify both sides of the equation after the subtraction.
$-3q - 14 = 10$

STEP 6

Next, we want to isolate the term with $q$ by getting rid of the constant on the left side. We will add $14$ to both sides of the equation.
$-3q - 14 + 14 = 10 + 14$

STEP 7

Simplify both sides of the equation after the addition.
$-3q = 24$

STEP 8

Now, to solve for $q$ , we will divide both sides of the equation by $-3$ .
$\frac{-3q}{-3} = \frac{24}{-3}$

STEP 9

Simplify both sides of the equation after the division.
$q = -8$
The solution to the equation is $q = -8$ .

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Solve the linear system and find the value of qqq.

STEP 1

Assumptions1. We are given an equation that needs to be simplified and solved for the variable qqq.2. The operations allowed are addition, subtraction, multiplication, and division.3. We will follow the order of operations and properties of equality to solve the equation.

STEP 2

First, we need to simplify the left side of the equation by combining like terms.−9q+8q=−1q-9q + 8q = -1q−9q+8q=−1q

STEP 3

Now, rewrite the equation with the simplified left side.−1q−14=2q+10-1q - 14 = 2q + 10−1q−14=2q+10

STEP 4

Next, we want to isolate the variable qqq on one side of the equation. To do this, we will subtract 2q2q2q from both sides of the equation to move all the qqq terms to the left side.−1q−2q−14=2q−2q+10-1q - 2q - 14 = 2q - 2q + 10−1q−2q−14=2q−2q+10

STEP 5

Simplify both sides of the equation after the subtraction.−3q−14=10-3q - 14 = 10−3q−14=10

STEP 6

Next, we want to isolate the term with qqq by getting rid of the constant on the left side. We will add 141414 to both sides of the equation.−3q−14+14=10+14-3q - 14 + 14 = 10 + 14−3q−14+14=10+14

STEP 7

Simplify both sides of the equation after the addition.−3q=24-3q = 24−3q=24

STEP 8

Now, to solve for qqq, we will divide both sides of the equation by −3-3−3.−3q−3=24−3\frac{-3q}{-3} = \frac{24}{-3}−3−3q​=−324​

STEP 9

Simplify both sides of the equation after the division.q=−8q = -8q=−8The solution to the equation is q=−8q = -8q=−8.

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Solve the linear system and find the value of $q$ .

Assumptions
1. We are given an equation that needs to be simplified and solved for the variable $q$ .
2. The operations allowed are addition, subtraction, multiplication, and division.
3. We will follow the order of operations and properties of equality to solve the equation.

First, we need to simplify the left side of the equation by combining like terms.
$-9q + 8q = -1q$

Now, rewrite the equation with the simplified left side.
$-1q - 14 = 2q + 10$

Next, we want to isolate the variable $q$ on one side of the equation. To do this, we will subtract $2q$ from both sides of the equation to move all the $q$ terms to the left side.
$-1q - 2q - 14 = 2q - 2q + 10$

Simplify both sides of the equation after the subtraction.
$-3q - 14 = 10$

Next, we want to isolate the term with $q$ by getting rid of the constant on the left side. We will add $14$ to both sides of the equation.
$-3q - 14 + 14 = 10 + 14$

Simplify both sides of the equation after the addition.
$-3q = 24$

Now, to solve for $q$ , we will divide both sides of the equation by $-3$ .
$\frac{-3q}{-3} = \frac{24}{-3}$

Simplify both sides of the equation after the division.
$q = -8$
The solution to the equation is $q = -8$ .