Solved on Dec 07, 2023

Solve $3(2 g+2.5)=15.9$ for $g$ . Determine if the given solution is correct and find the correct value of $g$ .

STEP 1

Assumptions
1. The original equation is $3(2g + 2.5) = 15.9$ .
2. The goal is to solve for the variable $g$ .
3. The steps provided in the problem statement are to be verified for correctness.

STEP 2

Let's first verify the steps provided in the problem statement.
The first step is to distribute the 3 across the terms inside the parentheses:
$3(2g + 2.5) = 15.9$

STEP 3

Distribute the 3 to both terms inside the parentheses:
$3 \cdot 2g + 3 \cdot 2.5 = 15.9$

STEP 4

Perform the multiplication:
$6g + 7.5 = 15.9$

STEP 5

Now, let's identify the error in the provided steps. The next step in the problem statement incorrectly states:
$6g = 23.4$
This is incorrect because the correct step should involve subtracting 7.5 from both sides of the equation to isolate the term with $g$ .

STEP 6

Subtract 7.5 from both sides of the equation to isolate the $6g$ term:
$6g + 7.5 - 7.5 = 15.9 - 7.5$

STEP 7

Perform the subtraction:
$6g = 15.9 - 7.5$

STEP 8

Calculate the right side of the equation:
$6g = 8.4$

STEP 9

Now, to solve for $g$ , divide both sides of the equation by 6:
$\frac{6g}{6} = \frac{8.4}{6}$

STEP 10

Perform the division:
$g = 1.4$

STEP 11

To verify the solution, plug $g = 1.4$ back into the original equation:
$3(2(1.4) + 2.5) = 15.9$

STEP 12

First, calculate the value inside the parentheses:
$2(1.4) + 2.5 = 2.8 + 2.5$

STEP 13

Add the values:
$2.8 + 2.5 = 5.3$

STEP 14

Now, multiply this result by 3:
$3 \cdot 5.3 = 15.9$

STEP 15

Perform the multiplication:
$15.9 = 15.9$

STEP 16

Since the left side of the equation equals the right side, our solution for $g$ is verified.
a) The provided steps are incorrect because the subtraction step was not performed correctly.
b) The correct value of $g$ is $1.4$ , and the verification shows that this solution satisfies the original equation.

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Solve $3(2 g+2.5)=15.9$ for $g$ . Determine if the given solution is correct and find the correct value of $g$ .

STEP 1

Assumptions
1. The original equation is $3(2g + 2.5) = 15.9$ .
2. The goal is to solve for the variable $g$ .
3. The steps provided in the problem statement are to be verified for correctness.

STEP 2

Let's first verify the steps provided in the problem statement.
The first step is to distribute the 3 across the terms inside the parentheses:
$3(2g + 2.5) = 15.9$

STEP 3

Distribute the 3 to both terms inside the parentheses:
$3 \cdot 2g + 3 \cdot 2.5 = 15.9$

STEP 4

Perform the multiplication:
$6g + 7.5 = 15.9$

STEP 5

Now, let's identify the error in the provided steps. The next step in the problem statement incorrectly states:
$6g = 23.4$
This is incorrect because the correct step should involve subtracting 7.5 from both sides of the equation to isolate the term with $g$ .

STEP 6

Subtract 7.5 from both sides of the equation to isolate the $6g$ term:
$6g + 7.5 - 7.5 = 15.9 - 7.5$

STEP 7

Perform the subtraction:
$6g = 15.9 - 7.5$

STEP 8

Calculate the right side of the equation:
$6g = 8.4$

STEP 9

Now, to solve for $g$ , divide both sides of the equation by 6:
$\frac{6g}{6} = \frac{8.4}{6}$

STEP 10

Perform the division:
$g = 1.4$

STEP 11

To verify the solution, plug $g = 1.4$ back into the original equation:
$3(2(1.4) + 2.5) = 15.9$

STEP 12

First, calculate the value inside the parentheses:
$2(1.4) + 2.5 = 2.8 + 2.5$

STEP 13

Add the values:
$2.8 + 2.5 = 5.3$

STEP 14

Now, multiply this result by 3:
$3 \cdot 5.3 = 15.9$

STEP 15

Perform the multiplication:
$15.9 = 15.9$

STEP 16

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Solve 3(2g+2.5)=15.93(2 g+2.5)=15.93(2g+2.5)=15.9 for ggg. Determine if the given solution is correct and find the correct value of ggg.

STEP 1

Assumptions1. The original equation is 3(2g+2.5)=15.93(2g + 2.5) = 15.93(2g+2.5)=15.9.2. The goal is to solve for the variable ggg.3. The steps provided in the problem statement are to be verified for correctness.

STEP 2

Let's first verify the steps provided in the problem statement.The first step is to distribute the 3 across the terms inside the parentheses:3(2g+2.5)=15.93(2g + 2.5) = 15.93(2g+2.5)=15.9

STEP 3

Distribute the 3 to both terms inside the parentheses:3⋅2g+3⋅2.5=15.93 \cdot 2g + 3 \cdot 2.5 = 15.93⋅2g+3⋅2.5=15.9

STEP 4

Perform the multiplication:6g+7.5=15.96g + 7.5 = 15.96g+7.5=15.9

STEP 5

Now, let's identify the error in the provided steps. The next step in the problem statement incorrectly states:6g=23.46g = 23.46g=23.4This is incorrect because the correct step should involve subtracting 7.5 from both sides of the equation to isolate the term with ggg.

STEP 6

Subtract 7.5 from both sides of the equation to isolate the 6g6g6g term:6g+7.5−7.5=15.9−7.56g + 7.5 - 7.5 = 15.9 - 7.56g+7.5−7.5=15.9−7.5

STEP 7

Perform the subtraction:6g=15.9−7.56g = 15.9 - 7.56g=15.9−7.5

STEP 8

Calculate the right side of the equation:6g=8.46g = 8.46g=8.4

STEP 9

Now, to solve for ggg, divide both sides of the equation by 6:6g6=8.46\frac{6g}{6} = \frac{8.4}{6}66g​=68.4​

STEP 10

Perform the division:g=1.4g = 1.4g=1.4

STEP 11

To verify the solution, plug g=1.4g = 1.4g=1.4 back into the original equation:3(2(1.4)+2.5)=15.93(2(1.4) + 2.5) = 15.93(2(1.4)+2.5)=15.9

STEP 12

First, calculate the value inside the parentheses:2(1.4)+2.5=2.8+2.52(1.4) + 2.5 = 2.8 + 2.52(1.4)+2.5=2.8+2.5

STEP 13

Add the values:2.8+2.5=5.32.8 + 2.5 = 5.32.8+2.5=5.3

STEP 14

Now, multiply this result by 3:3⋅5.3=15.93 \cdot 5.3 = 15.93⋅5.3=15.9

STEP 15

Perform the multiplication:15.9=15.915.9 = 15.915.9=15.9

STEP 16

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Solve $3(2 g+2.5)=15.9$ for $g$ . Determine if the given solution is correct and find the correct value of $g$ .

Assumptions
1. The original equation is $3(2g + 2.5) = 15.9$ .
2. The goal is to solve for the variable $g$ .
3. The steps provided in the problem statement are to be verified for correctness.

Let's first verify the steps provided in the problem statement.
The first step is to distribute the 3 across the terms inside the parentheses:
$3(2g + 2.5) = 15.9$

Distribute the 3 to both terms inside the parentheses:
$3 \cdot 2g + 3 \cdot 2.5 = 15.9$

Perform the multiplication:
$6g + 7.5 = 15.9$

Now, let's identify the error in the provided steps. The next step in the problem statement incorrectly states:
$6g = 23.4$
This is incorrect because the correct step should involve subtracting 7.5 from both sides of the equation to isolate the term with $g$ .

Subtract 7.5 from both sides of the equation to isolate the $6g$ term:
$6g + 7.5 - 7.5 = 15.9 - 7.5$

Perform the subtraction:
$6g = 15.9 - 7.5$

Calculate the right side of the equation:
$6g = 8.4$

Now, to solve for $g$ , divide both sides of the equation by 6:
$\frac{6g}{6} = \frac{8.4}{6}$

Perform the division:
$g = 1.4$

To verify the solution, plug $g = 1.4$ back into the original equation:
$3(2(1.4) + 2.5) = 15.9$

First, calculate the value inside the parentheses:
$2(1.4) + 2.5 = 2.8 + 2.5$

Add the values:
$2.8 + 2.5 = 5.3$

Now, multiply this result by 3:
$3 \cdot 5.3 = 15.9$

Perform the multiplication:
$15.9 = 15.9$