Solved on Feb 23, 2024

Solve $15(5c-7) = 9c-9$ using addition and multiplication. Find the correct value from the options: $\frac{114}{11}, \frac{16}{11}, \frac{4}{21}$ .

STEP 1

Assumptions
1. We are given the equation $15(5c - 7) = 9c - 9$ .
2. We need to solve for the variable $c$ .
3. The solution must match one of the given options: a. $\frac{114}{11}$ , b. $\frac{16}{11}$ , c. $\frac{4}{21}$ .

STEP 2

First, we need to distribute the multiplication over the subtraction inside the parentheses.
$15(5c - 7) = 15 \cdot 5c - 15 \cdot 7$

STEP 3

Now, perform the multiplication to simplify the left side of the equation.
$15 \cdot 5c = 75c$ $15 \cdot 7 = 105$
$75c - 105 = 9c - 9$

STEP 4

Next, we want to get all the terms with the variable $c$ on one side of the equation and the constants on the other side. We can do this by subtracting $9c$ from both sides of the equation.
$75c - 105 - 9c = 9c - 9 - 9c$

STEP 5

Combine like terms on both sides of the equation.
$75c - 9c = 66c$ $-105 = -9$
$66c - 105 = -9$

STEP 6

Now, we want to isolate the variable $c$ . We can do this by adding $105$ to both sides of the equation to move the constant to the right side.
$66c - 105 + 105 = -9 + 105$

STEP 7

Simplify both sides of the equation.
$66c = 96$

STEP 8

To solve for $c$ , we need to divide both sides of the equation by $66$ .
$\frac{66c}{66} = \frac{96}{66}$

STEP 9

Simplify the fraction on the right side of the equation to find the value of $c$ .
$c = \frac{96}{66}$

STEP 10

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $6$ .
$c = \frac{96 \div 6}{66 \div 6}$

STEP 11

Calculate the reduced fraction.
$c = \frac{16}{11}$
The value of $c$ is $\frac{16}{11}$ , which matches option b.

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Solve $15(5c-7) = 9c-9$ using addition and multiplication. Find the correct value from the options: $\frac{114}{11}, \frac{16}{11}, \frac{4}{21}$ .

STEP 1

Assumptions
1. We are given the equation $15(5c - 7) = 9c - 9$ .
2. We need to solve for the variable $c$ .
3. The solution must match one of the given options: a. $\frac{114}{11}$ , b. $\frac{16}{11}$ , c. $\frac{4}{21}$ .

STEP 2

First, we need to distribute the multiplication over the subtraction inside the parentheses.
$15(5c - 7) = 15 \cdot 5c - 15 \cdot 7$

STEP 3

Now, perform the multiplication to simplify the left side of the equation.
$15 \cdot 5c = 75c$ $15 \cdot 7 = 105$
$75c - 105 = 9c - 9$

STEP 4

Next, we want to get all the terms with the variable $c$ on one side of the equation and the constants on the other side. We can do this by subtracting $9c$ from both sides of the equation.
$75c - 105 - 9c = 9c - 9 - 9c$

STEP 5

Combine like terms on both sides of the equation.
$75c - 9c = 66c$ $-105 = -9$
$66c - 105 = -9$

STEP 6

Now, we want to isolate the variable $c$ . We can do this by adding $105$ to both sides of the equation to move the constant to the right side.
$66c - 105 + 105 = -9 + 105$

STEP 7

Simplify both sides of the equation.
$66c = 96$

STEP 8

To solve for $c$ , we need to divide both sides of the equation by $66$ .
$\frac{66c}{66} = \frac{96}{66}$

STEP 9

Simplify the fraction on the right side of the equation to find the value of $c$ .
$c = \frac{96}{66}$

STEP 10

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $6$ .
$c = \frac{96 \div 6}{66 \div 6}$

STEP 11

Calculate the reduced fraction.
$c = \frac{16}{11}$
The value of $c$ is $\frac{16}{11}$ , which matches option b.

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Solve 15(5c−7)=9c−915(5c-7) = 9c-915(5c−7)=9c−9 using addition and multiplication. Find the correct value from the options: 11411,1611,421\frac{114}{11}, \frac{16}{11}, \frac{4}{21}11114​,1116​,214​.

STEP 1

Assumptions1. We are given the equation 15(5c−7)=9c−915(5c - 7) = 9c - 915(5c−7)=9c−9.2. We need to solve for the variable ccc.3. The solution must match one of the given options: a. 11411\frac{114}{11}11114​, b. 1611\frac{16}{11}1116​, c. 421\frac{4}{21}214​.

STEP 2

First, we need to distribute the multiplication over the subtraction inside the parentheses.15(5c−7)=15⋅5c−15⋅715(5c - 7) = 15 \cdot 5c - 15 \cdot 715(5c−7)=15⋅5c−15⋅7

STEP 3

Now, perform the multiplication to simplify the left side of the equation.15⋅5c=75c15 \cdot 5c = 75c15⋅5c=75c 15⋅7=10515 \cdot 7 = 10515⋅7=10575c−105=9c−975c - 105 = 9c - 975c−105=9c−9

STEP 4

Next, we want to get all the terms with the variable ccc on one side of the equation and the constants on the other side. We can do this by subtracting 9c9c9c from both sides of the equation.75c−105−9c=9c−9−9c75c - 105 - 9c = 9c - 9 - 9c75c−105−9c=9c−9−9c

STEP 5

Combine like terms on both sides of the equation.75c−9c=66c75c - 9c = 66c75c−9c=66c −105=−9-105 = -9−105=−966c−105=−966c - 105 = -966c−105=−9

STEP 6

Now, we want to isolate the variable ccc. We can do this by adding 105105105 to both sides of the equation to move the constant to the right side.66c−105+105=−9+10566c - 105 + 105 = -9 + 10566c−105+105=−9+105

STEP 7

Simplify both sides of the equation.66c=9666c = 9666c=96

STEP 8

To solve for ccc, we need to divide both sides of the equation by 666666.66c66=9666\frac{66c}{66} = \frac{96}{66}6666c​=6696​

STEP 9

Simplify the fraction on the right side of the equation to find the value of ccc.c=9666c = \frac{96}{66}c=6696​

STEP 10

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 666.c=96÷666÷6c = \frac{96 \div 6}{66 \div 6}c=66÷696÷6​

STEP 11

Calculate the reduced fraction.c=1611c = \frac{16}{11}c=1116​The value of ccc is 1611\frac{16}{11}1116​, which matches option b.

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Solve $15(5c-7) = 9c-9$ using addition and multiplication. Find the correct value from the options: $\frac{114}{11}, \frac{16}{11}, \frac{4}{21}$ .

Assumptions
1. We are given the equation $15(5c - 7) = 9c - 9$ .
2. We need to solve for the variable $c$ .
3. The solution must match one of the given options: a. $\frac{114}{11}$ , b. $\frac{16}{11}$ , c. $\frac{4}{21}$ .

First, we need to distribute the multiplication over the subtraction inside the parentheses.
$15(5c - 7) = 15 \cdot 5c - 15 \cdot 7$

Now, perform the multiplication to simplify the left side of the equation.
$15 \cdot 5c = 75c$ $15 \cdot 7 = 105$
$75c - 105 = 9c - 9$

Next, we want to get all the terms with the variable $c$ on one side of the equation and the constants on the other side. We can do this by subtracting $9c$ from both sides of the equation.
$75c - 105 - 9c = 9c - 9 - 9c$

Combine like terms on both sides of the equation.
$75c - 9c = 66c$ $-105 = -9$
$66c - 105 = -9$

Now, we want to isolate the variable $c$ . We can do this by adding $105$ to both sides of the equation to move the constant to the right side.
$66c - 105 + 105 = -9 + 105$

Simplify both sides of the equation.
$66c = 96$

To solve for $c$ , we need to divide both sides of the equation by $66$ .
$\frac{66c}{66} = \frac{96}{66}$

Simplify the fraction on the right side of the equation to find the value of $c$ .
$c = \frac{96}{66}$

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $6$ .
$c = \frac{96 \div 6}{66 \div 6}$

Calculate the reduced fraction.
$c = \frac{16}{11}$
The value of $c$ is $\frac{16}{11}$ , which matches option b.