Solved on Jan 07, 2024

Solve for $x$ using addition and multiplication principles, given $-\frac{7}{3} x+\frac{1}{3}=-9$ .

STEP 1

Assumptions
1. We are given the equation $-\frac{7}{3} x + \frac{1}{3} = -9$ .
2. We will use the addition and multiplication principles to solve for $x$ .
3. The addition principle states that we can add or subtract the same value from both sides of an equation without changing the solution.
4. The multiplication principle states that we can multiply or divide both sides of an equation by the same nonzero value without changing the solution.

STEP 2

First, we want to eliminate the fraction on the left side of the equation by multiplying both sides of the equation by the least common denominator, which in this case is 3.
$3 \left( -\frac{7}{3} x + \frac{1}{3} \right) = 3(-9)$

STEP 3

Distribute the multiplication across the terms on the left side of the equation.
$-7x + 1 = -27$

STEP 4

Now, we will isolate the variable $x$ by using the addition principle to move the constant term from the left side to the right side of the equation. We do this by adding $-1$ to both sides of the equation.
$-7x + 1 - 1 = -27 - 1$

STEP 5

Simplify both sides of the equation.
$-7x = -28$

STEP 6

Next, we will use the multiplication principle to solve for $x$ . We do this by dividing both sides of the equation by $-7$ .
$\frac{-7x}{-7} = \frac{-28}{-7}$

STEP 7

Simplify both sides of the equation to find the value of $x$ .
$x = 4$
The solution to the equation $-\frac{7}{3} x + \frac{1}{3} = -9$ is $x = 4$ .

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Solve for $x$ using addition and multiplication principles, given $-\frac{7}{3} x+\frac{1}{3}=-9$ .

STEP 1

STEP 2

First, we want to eliminate the fraction on the left side of the equation by multiplying both sides of the equation by the least common denominator, which in this case is 3.
$3 \left( -\frac{7}{3} x + \frac{1}{3} \right) = 3(-9)$

STEP 3

Distribute the multiplication across the terms on the left side of the equation.
$-7x + 1 = -27$

STEP 4

Now, we will isolate the variable $x$ by using the addition principle to move the constant term from the left side to the right side of the equation. We do this by adding $-1$ to both sides of the equation.
$-7x + 1 - 1 = -27 - 1$

STEP 5

Simplify both sides of the equation.
$-7x = -28$

STEP 6

Next, we will use the multiplication principle to solve for $x$ . We do this by dividing both sides of the equation by $-7$ .
$\frac{-7x}{-7} = \frac{-28}{-7}$

STEP 7

Simplify both sides of the equation to find the value of $x$ .
$x = 4$
The solution to the equation $-\frac{7}{3} x + \frac{1}{3} = -9$ is $x = 4$ .

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Solve for xxx using addition and multiplication principles, given −73x+13=−9-\frac{7}{3} x+\frac{1}{3}=-9−37​x+31​=−9.

STEP 1

STEP 2

First, we want to eliminate the fraction on the left side of the equation by multiplying both sides of the equation by the least common denominator, which in this case is 3.3(−73x+13)=3(−9)3 \left( -\frac{7}{3} x + \frac{1}{3} \right) = 3(-9)3(−37​x+31​)=3(−9)

STEP 3

Distribute the multiplication across the terms on the left side of the equation.−7x+1=−27-7x + 1 = -27−7x+1=−27

STEP 4

Now, we will isolate the variable xxx by using the addition principle to move the constant term from the left side to the right side of the equation. We do this by adding −1-1−1 to both sides of the equation.−7x+1−1=−27−1-7x + 1 - 1 = -27 - 1−7x+1−1=−27−1

STEP 5

Simplify both sides of the equation.−7x=−28-7x = -28−7x=−28

STEP 6

Next, we will use the multiplication principle to solve for xxx. We do this by dividing both sides of the equation by −7-7−7.−7x−7=−28−7\frac{-7x}{-7} = \frac{-28}{-7}−7−7x​=−7−28​

STEP 7

Simplify both sides of the equation to find the value of xxx.x=4x = 4x=4The solution to the equation −73x+13=−9-\frac{7}{3} x + \frac{1}{3} = -9−37​x+31​=−9 is x=4x = 4x=4.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve for $x$ using addition and multiplication principles, given $-\frac{7}{3} x+\frac{1}{3}=-9$ .

First, we want to eliminate the fraction on the left side of the equation by multiplying both sides of the equation by the least common denominator, which in this case is 3.
$3 \left( -\frac{7}{3} x + \frac{1}{3} \right) = 3(-9)$

Distribute the multiplication across the terms on the left side of the equation.
$-7x + 1 = -27$

Now, we will isolate the variable $x$ by using the addition principle to move the constant term from the left side to the right side of the equation. We do this by adding $-1$ to both sides of the equation.
$-7x + 1 - 1 = -27 - 1$

Simplify both sides of the equation.
$-7x = -28$

Next, we will use the multiplication principle to solve for $x$ . We do this by dividing both sides of the equation by $-7$ .
$\frac{-7x}{-7} = \frac{-28}{-7}$

Simplify both sides of the equation to find the value of $x$ .
$x = 4$
The solution to the equation $-\frac{7}{3} x + \frac{1}{3} = -9$ is $x = 4$ .