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3 years ago

What is the first step you will use to solve this equation:

1 answer:

5 0

Subtract 4x from both sides

4x +2 = 7x - 13 would then simplify to

3x - 13 = 2 ( you can switch the problem around as long as you dont switch the variables around )

then you have to + 13 which simplifies to

3x = 15

then you divide by 3 which equals

x=5

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3 years ago

The mean room temperature from Monday to Saturday is 25oC and the mean room temperature of Saturday and Sunday is 28oC. if the m

Thepotemich [5.8K]

Answer:

We can conclude that the room temperature on Saturday was 24°C

Step-by-step explanation:

For a set of N values:

{x₁, x₂, ..., xₙ}

The mean of the set is calculated as:

$M = \frac{x_1 + x_2 + ... + x_n}{N}$

In this case, our set is the temperature of 7 days (so we have 7 elements)

{T₁, T₂, T₃, T₄, T₅, T₆, T₇}

Such that:

T₆ = temperature on Saturday

T₇ = temperature on Sunday.

We know that:

"The mean room temperature from Monday to Saturday is 25°C"

Then:

$\frac{T_1 + T_2 + T_3 + T_4 + T_5 + T_6}{6} = 25 C$

"the mean room temperature of Saturday and Sunday is 28°C"

$\frac{T_6 + T_7}{2} = 28C$

"The mean room temperature from Monday to Sunday is 26°C"

$\frac{T_1 + T_2 + T_3 + T_4 + T_5 + T_6 + T_7}{7} = 26 C$

So we have 3 equations.

Let's rewrite:

T₁ + T₂ + T₃ + T₄ + T₅ = A

Then we can rewrite our equations as:

$\frac{A+ T_6}{6} = 25 C$

$\frac{T_6 + T_7}{2} = 28C$

$\frac{A + T_6 + T_7}{7} = 26 C$

Removing the "Celcius" and multiplying in the 3 equations by the denominator on both sides, we get:

A + T₆ = 6*25

T₆ + T₇ = 2*28

A + T₆ + T₇ = 7*26

We now need to solve that system for T₆

The first step is to isolate one of the variables in one of the equations, (because we want to solve this for T₆ , let's not isolate that one). Let's isolate A in the first one:

A = 6*25 - T₆

A = 150 - T₆

Now we can replace this on the other two equations:

T₆ + T₇ = 2*28

(150 - T₆ ) + T₆ + T₇ = 7*26

Now, let's isolate T₇ in the top equation to get:

T₇ = 2*28 - T₆

T₇ = 56 - T₆

Now we can replace this in the last equation to get:

(150 - T₆ ) + T₆ + (56 - T₆) = 7*26

Now, we can solve this for T₆

150 - T₆ + T₆ + 56 - T₆ = 182

-T₆ = 182 - 150 - 56

-T₆ = -24

T₆ = 24

We can conclude that the room temperature on Saturday was 24°C

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