Solved on Jan 23, 2024

Solve the linear equation $8c + 2(3c + 3) = 12$ and find the solution set.
Part 1 of 2 Identify as an expression or an equation. This is an equation.
Part 2 of 2 The solution set is $c = 1$ .

STEP 1

Assumptions
1. The given mathematical statement is an equation because it contains an equals sign.
2. We need to solve for the variable $c$ .

STEP 2

First, we need to simplify the left-hand side of the equation by distributing the multiplication over the addition within the parentheses.
$8c + 2(3c + 3) = 12$

STEP 3

Apply the distributive property $a(b + c) = ab + ac$ .
$8c + 2 \cdot 3c + 2 \cdot 3 = 12$

STEP 4

Perform the multiplication.
$8c + 6c + 6 = 12$

STEP 5

Combine like terms on the left-hand side.
$14c + 6 = 12$

STEP 6

Subtract 6 from both sides of the equation to isolate the term with the variable $c$ .
$14c + 6 - 6 = 12 - 6$

STEP 7

Simplify both sides of the equation.
$14c = 6$

STEP 8

Divide both sides of the equation by 14 to solve for $c$ .
$\frac{14c}{14} = \frac{6}{14}$

STEP 9

Simplify the fraction on the right-hand side by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$c = \frac{6}{14} = \frac{3}{7}$
The solution set is $\{ \frac{3}{7} \}$ .

Was this helpful?

Solve the linear equation $8c + 2(3c + 3) = 12$ and find the solution set.
Part 1 of 2 Identify as an expression or an equation. This is an equation.
Part 2 of 2 The solution set is $c = 1$ .

STEP 1

Assumptions
1. The given mathematical statement is an equation because it contains an equals sign.
2. We need to solve for the variable $c$ .

STEP 2

First, we need to simplify the left-hand side of the equation by distributing the multiplication over the addition within the parentheses.
$8c + 2(3c + 3) = 12$

STEP 3

Apply the distributive property $a(b + c) = ab + ac$ .
$8c + 2 \cdot 3c + 2 \cdot 3 = 12$

STEP 4

Perform the multiplication.
$8c + 6c + 6 = 12$

STEP 5

Combine like terms on the left-hand side.
$14c + 6 = 12$

STEP 6

Subtract 6 from both sides of the equation to isolate the term with the variable $c$ .
$14c + 6 - 6 = 12 - 6$

STEP 7

Simplify both sides of the equation.
$14c = 6$

STEP 8

Divide both sides of the equation by 14 to solve for $c$ .
$\frac{14c}{14} = \frac{6}{14}$

STEP 9

Simplify the fraction on the right-hand side by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$c = \frac{6}{14} = \frac{3}{7}$
The solution set is $\{ \frac{3}{7} \}$ .

Start learning now

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

Solve the linear equation 8c+2(3c+3)=128c + 2(3c + 3) = 128c+2(3c+3)=12 and find the solution set.Part 1 of 2 Identify as an expression or an equation. This is an equation.Part 2 of 2 The solution set is c=1c = 1c=1.

STEP 1

Assumptions1. The given mathematical statement is an equation because it contains an equals sign.2. We need to solve for the variable ccc.

STEP 2

First, we need to simplify the left-hand side of the equation by distributing the multiplication over the addition within the parentheses.8c+2(3c+3)=128c + 2(3c + 3) = 128c+2(3c+3)=12

STEP 3

Apply the distributive property a(b+c)=ab+aca(b + c) = ab + aca(b+c)=ab+ac.8c+2⋅3c+2⋅3=128c + 2 \cdot 3c + 2 \cdot 3 = 128c+2⋅3c+2⋅3=12

STEP 4

Perform the multiplication.8c+6c+6=128c + 6c + 6 = 128c+6c+6=12

STEP 5

Combine like terms on the left-hand side.14c+6=1214c + 6 = 1214c+6=12

STEP 6

Subtract 6 from both sides of the equation to isolate the term with the variable ccc.14c+6−6=12−614c + 6 - 6 = 12 - 614c+6−6=12−6

STEP 7

Simplify both sides of the equation.14c=614c = 614c=6

STEP 8

Divide both sides of the equation by 14 to solve for ccc.14c14=614\frac{14c}{14} = \frac{6}{14}1414c​=146​

STEP 9

Simplify the fraction on the right-hand side by dividing both the numerator and the denominator by their greatest common divisor, which is 2.c=614=37c = \frac{6}{14} = \frac{3}{7}c=146​=73​The solution set is {37}\{ \frac{3}{7} \}{73​}.

Start learning now

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

Solve the linear equation $8c + 2(3c + 3) = 12$ and find the solution set.
Part 1 of 2 Identify as an expression or an equation. This is an equation.
Part 2 of 2 The solution set is $c = 1$ .

Assumptions
1. The given mathematical statement is an equation because it contains an equals sign.
2. We need to solve for the variable $c$ .

First, we need to simplify the left-hand side of the equation by distributing the multiplication over the addition within the parentheses.
$8c + 2(3c + 3) = 12$

Apply the distributive property $a(b + c) = ab + ac$ .
$8c + 2 \cdot 3c + 2 \cdot 3 = 12$

Perform the multiplication.
$8c + 6c + 6 = 12$

Combine like terms on the left-hand side.
$14c + 6 = 12$

Subtract 6 from both sides of the equation to isolate the term with the variable $c$ .
$14c + 6 - 6 = 12 - 6$

Simplify both sides of the equation.
$14c = 6$

Divide both sides of the equation by 14 to solve for $c$ .
$\frac{14c}{14} = \frac{6}{14}$

Simplify the fraction on the right-hand side by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$c = \frac{6}{14} = \frac{3}{7}$
The solution set is $\{ \frac{3}{7} \}$ .