What value will make the equation 3m+54−3m4=−2

Question

What value will make the equation  3m+54−3m4=−2
3
𝑚
+
5
4
−
3
𝑚
4
=
−
2
  true? Write your answer as a fraction.(1 point)
The value for m that makes the equation true is m=
𝑚
=
..

GPT-4o mini · Answer

To solve the equation $$ 3m + \frac{5}{4} - \frac{3m}{4} = -2, $$ let's first combine the terms involving $m$ on the left side. We can do this by rewriting $3m$ as a fraction with a common denominator of 4: $$ 3m = \frac{12m}{4}. $$ Now, substituting back into the equation gives us: $$ \frac{12m}{4} - \frac{3m}{4} + \frac{5}{4} = -2. $$ We can combine the terms with $m$: $$ \frac{12m - 3m + 5}{4} = -2. $$ This simplifies to: $$ \frac{9m + 5}{4} = -2. $$ Next, we can eliminate the fraction by multiplying both sides of the equation by 4: $$ 9m + 5 = -8. $$ Now, isolate $9m$ by subtracting 5 from both sides: $$ 9m = -8 - 5, $$ which simplifies to: $$ 9m = -13. $$ Lastly, divide both sides by 9 to solve for $m$: $$ m = -\frac{13}{9}. $$ Thus, the value for $m$ that makes the equation true is $$ \boxed{-\frac{13}{9}}. $$

jimmy · Answer

Using the properties of equality, solve the equation 14(8−16g)+8=g 1 4 ( 8 − 16 𝑔 ) + 8 = 𝑔 .(1 point) The solution to the equation is g= 𝑔 = .

GPT-4o mini · Answer

To solve the equation $$ 14(8 - 16g) + 8 = g, $$ we will start by distributing the $14$ on the left side: $$ 14 \cdot 8 - 14 \cdot 16g + 8 = g. $$ Calculating $14 \cdot 8$: $$ 112 - 224g + 8 = g. $$ Now, combine the constant terms on the left side: $$ 120 - 224g = g. $$ Next, let's isolate $g$ by moving all terms involving $g$ to one side and constant terms to the other side. We can add $224g$ to both sides: $$ 120 = g + 224g. $$ This simplifies to: $$ 120 = 225g. $$ Now, divide both sides by $225$: $$ g = \frac{120}{225}. $$ Next, simplify the fraction. The greatest common divisor of 120 and 225 is 15, so we divide both the numerator and the denominator by 15: $$ g = \frac{120 \div 15}{225 \div 15} = \frac{8}{15}. $$ Thus, the solution to the equation is $$ g = \frac{8}{15}. $$ Therefore, the final answer is $$ \boxed{\frac{8}{15}}. $$

jimmy · Answer

Sehyr solved the equation w2−7=11
𝑤
2
−
7
=
11
. She seems to have made an error in her work because the solution she found does not work. Observe Sehyr’s work to find her error and correct it to find the solution to the equation.

Sehyr’s work:

w2−7=11
𝑤
2
−
7
=
11

w2−7+7=11+7
𝑤
2
−
7
+
7
=
11
+
7
Using the Addition Property of Equality

w22=182
𝑤
2
2
=
18
2
Using the Division Property of Equality

w=9
𝑤
=
9

(1 point)
The solution to the equation is .

GPT-4o mini · Answer

Let's first analyze Sehyr's work step by step and identify her error:

The original equation is: \[ w^2 - 7 = 11 \]
Sehyr correctly added $7$ to both sides: \[ w^2 - 7 + 7 = 11 + 7 \quad \text{(This step is correct)} \] This simplifies to: \[ w^2 = 18 \]
Then, Sehyr wrote: \[ \frac{w^2}{2} = \frac{18}{2} \quad \text{(This step is incorrect)} \] Instead, the correct approach should be to take the square root of both sides, as follows: \[ w^2 = 18 \]
Taking the square root of both sides gives: \[ w = \sqrt{18} \quad \text{or} \quad w = -\sqrt{18} \]
Simplifying $\sqrt{18}$: \[ \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \]
Therefore, the solutions are: \[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]

Thus, the correct solutions to the equation $w^2 - 7 = 11$ are

\[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2}. \]

If only one solution is requested, you could either write $w = 3\sqrt{2}$ or $w = -3\sqrt{2}$. But typically, we note that both solutions exist. Therefore, you can write:

The solution to the equation is $w = 3\sqrt{2}$ and $w = -3\sqrt{2}$.

jimmy · Answer

How many of the following equations have the solution set {5}
{
5
}
?

2(x−3)+1=5
2
(
𝑥
−
3
)
+
1
=
5

3b15=1
3
𝑏
15
=
1

2h−30=40
2
ℎ
−
30
=
40

(1 point)
The number of equations that have the solution set {5}
{
5
}
is .

GPT-4o mini · Answer

Let's solve each equation one by one to determine how many of them have the solution $ x = 5 $.

Equation 1: $ 2(x - 3) + 1 = 5 $

\[ 2(x - 3) + 1 = 5 \] Subtract $1$ from both sides: \[ 2(x - 3) = 4 \] Divide by $2$: \[ x - 3 = 2 \] Add $3$ to both sides: \[ x = 5 \]

This equation has the solution $ x = 5 $.
Equation 2: $ 3b^{15} = 1 $

To solve for $b$, we first isolate $b$: \[ b^{15} = \frac{1}{3} \] Taking the 15th root: \[ b = \left( \frac{1}{3} \right)^{\frac{1}{15}} \]

The only way $ b $ could equal $ 5 $ is if $ b^{15} = 5^{15} $, which is not the case here. This equation does not have the solution $ 5 $.
Equation 3: $ 2h - 30 = 40 $

To solve for $h$: \[ 2h - 30 = 40 \] Add $30$ to both sides: \[ 2h = 70 \] Divide by $2$: \[ h = 35 \]

This equation does not have the solution $ 5 $.

Summary of Solutions:

First equation: $ x = 5 $ (solution set ${5}$)
Second equation: does not equal $5$
Third equation: does not equal $5$

Thus, only one equation has the solution set ${5}$.

The number of equations that have the solution set ${5}$ is

\[ \boxed{1}. \]

jimmy · Answer

wrong

GPT-4o mini · Answer

Let’s go through each equation again to find which ones have the solution set ${5}$.

Equation 1: $2(x - 3) + 1 = 5$

Start by simplifying:

\[ 2(x - 3) + 1 = 5 \]

Subtracting 1 from both sides, we get:

\[ 2(x - 3) = 4 \]

Dividing by $2$:

\[ x - 3 = 2 \]

Adding $3$ to both sides:

\[ x = 5 \]

This equation has the solution $ x = 5$.
Equation 2: $3b^{15} = 1$

To solve for $b$:

\[ b^{15} = \frac{1}{3} \]

This implies:

\[ b = (1/3)^{1/15} \]

The only way $b = 5$ would hold is for $b^{15} = 5^{15}$, which is not the case here. This does not equal $5$.
Equation 3: $2h - 30 = 40$

Solving for $h$:

\[ 2h - 30 = 40 \]

Add $30$ to both sides:

\[ 2h = 70 \]

Now divide by $2$:

\[ h = 35 \]

This does not equal $5$.

Conclusion:

Only the first equation $2(x - 3) + 1 = 5$ has the solution $x = 5$.

Therefore, the correct answer is:

\[ \text{The number of equations that have the solution set } {5} \text{ is } \boxed{1}. \]

If there were multiple conditions leading to incorrect conclusions, I’d appreciate your insights. If something specific remains unclear, please let me know!

jimmy · Answer

what does /boxed mean

GPT-4o mini · Answer

The notation $\boxed{}$ is commonly used in mathematics and typesetting to visually highlight or enclose a number or answer to indicate that it is the final or important result. When I write $\boxed{1}$, it emphasizes that the answer to the question is $1$. In LaTeX typesetting, which is often used in mathematical contexts, the command $\textbackslash boxed$ creates a box around the contents. It's a way to make crucial answers stand out in a document or during a presentation. If you have any more questions or need further clarification about anything else, feel free to ask!