Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?

1 answer:

8 0

3[x + 3(4x - 5)] = 15x - 24
3(x + 12x - 15) = 15x - 24
3(13x - 15) = 15x - 24
39x - 45 = 15x - 24 |add 45 to both sides
39x = 15x + 21 |subtract 15x from both sides
24x = 21 |divide both sides by 24
x = 21/24
x = 7/8

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Given:

One linear function represented by the table.

Another linear function represented by the graph.

To find:

The greater unit rate and greater y-intercept.

Solution:

Formula for slope (unit rate):

$m=\dfrac{y_2-y_1}{x_2-x_1}$

From the given table it is clear that the linear function passes through (0,5) and (5,15). The function intersect the y-axis at (0,15), so the y-intercept is 15.

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$m_1=\dfrac{10}{5}$

$m_1=2$

So, the unit rate of first function is 2.

From the given graph it is clear that the linear function passes through (0,6) and (-4,0). The function intersect the y-axis at (0,6), so the y-intercept is 6.

$m_2=\dfrac{0-6}{-4-0}$