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3 years ago

What is the solution to the equation One-third (x minus 2) = one-fifth (x + 4) + 2? x = 12 x = 14 x = 16 x = 26

Mathematics

1 answer:

Elena L [17]3 years ago

3 0

Answer:

x = 26

Step-by-step explanation:

Given

$\frac{1}{3}$ (x - 2) = $\frac{1}{5}$ (x + 4) + 2

Multiply through by 15 to clear the fractions

5(x - 2) =3(x + 4) + 30 ← distribute and simplify both sides

5x - 10 = 3x + 12 + 30, that is

5x - 10 = 3x + 42 ( subtract 3x from both sides )

2x - 10 = 42 ( add 10 to both sides )

2x = 52 ( divide both sides by 2 )

x = 26

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<h3>Answer: A) Dashed line, shaded below</h3>

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Explanation:

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The graph of y < -0.5x+4 will be the same as the graph of 2x+4y < 16

To graph y < -0.5x+4, we graph y = -0.5x+4 which is a straight line that goes through the two points (0,4) and (2, 3). This is the boundary line of the inequality shaded region. The boundary line is a dashed line because we are not including points on the boundary that are part of the solution set. We only include these boundary points if the inequality sign has "or equal to".

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Perhaps another method to find what direction we shade is we can try out a point like (0,0). The point cannot be on the boundary line.

Plug those coordinates into either equation. I'll pick the second equation

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