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2 years ago

3x + 1 = 3(x - 1) + 4

Mathematics

1 answer:

Pavlova-9 [17]2 years ago

7 0

Simplifying

3x + 1 = 3[x + -1] + 4

Reorder the terms:

1 + 3x = 3[x + -1] + 4

Reorder the terms:

1 + 3x = 3[-1 + x] + 4

1 + 3x = [-1 * 3 + x * 3] + 4

1 + 3x = [-3 + 3x] + 4

Reorder the terms:

1 + 3x = -3 + 4 + 3x

Combine like terms: -3 + 4 = 1

1 + 3x = 1 + 3x

Add '-1' to each side of the equation.

1 + -1 + 3x = 1 + -1 + 3x

Combine like terms: 1 + -1 = 0

0 + 3x = 1 + -1 + 3x

3x = 1 + -1 + 3x

Combine like terms: 1 + -1 = 0

3x = 0 + 3x

3x = 3x

Add '-3x' to each side of the equation.

3x + -3x = 3x + -3x

Combine like terms: 3x + -3x = 0

0 = 3x + -3x

Combine like terms: 3x + -3x = 0

0 = 0

This equation is an identity, all real numbers are solutions.

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The Atlantic Salmon swim upstream at a steady rate of 2 miles every 3 minutes. Fill in the table to describe the relationship. R

Likurg_2 [28]

The distance traveled by the Salmon is proportional to the duration spent

swimming.

A table of the distance traveled by the Atlantic Salmon is presented as follows;

$\begin{tabular}{|c|c|c}\underline{Time in minutes}&\underline{Miles Traveled at 2/3 miles per minute } \\1&2/3 \\2&4/3\\3&2\\4&8/3\\5&10/3\\6&4\end{array}$

Reasons:

The given parameter are;

The steady rate at which Atlantic Salmon swims = 2 miles in 3 minutes

Distance the Salmon swims, d ∝ Time taken, t

Therefore;

d = s·t

Where;

s = The constant of proportionality = The speed

Which gives;

$\displaystyle s = \mathbf{\frac{Distance, \, d}{Time, \, t}}$

The speed with which the Atlantic Salmon swims per minute is therefore;

$\displaystyle The \ speed = \mathbf{\frac{2 \ miles}{3 \ minutes}} = \frac{2}{3} \ miles /minute$

The distance travelled, <em>d</em>, is given as follows;

$\displaystyle d = \mathbf{\frac{2}{3} \times t}$

A table showing the distance travelled by the fish with time is presented as follows;

$\begin{tabular}{|c|c|c|}\underline{Time, t, in minutes}&\underline{t \times d}&\underline{Miles Traveled, d, at 2/3 miles per minute } \\1&1 \times 2/3 = 2/3&2/3 \\2&2 \times 2/3 = 4/3&4/3\\3&3 \times 2/3 = 2&2\\4&4 \times 2/3 = 8/3&8/3\\5&5 \times 2/3 = 10/3&10/3\\6&6 \times 2/3 = 4&4\end{array}$