Solve each of the following equations. Show its solution set on a number line. Check your answers. 3 |2-x|=-6
2 answers:
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A) Answer: A. 22.5 cm, 30 cm, and 37.5 cm
Setting the unity measurement as x, the three sides will be 3·x, 4·x, and 5·x. The sum of the three sides will be (3 + 4 + 5)·x = 12·x; this corresponds to the perimeter, therefore:
12·x = 90 cm
We can solve for x:
x = 90 / 12 = 7.5 cm
Hence, the sides will be:
7.5 · 3 = 22.5 cm
7.5 · 4 = 30 cm
7.5 · 5 = 37.5 cm
This situation is represented in option A (which is also the only option whose sides add up to 90).
B) Answer: C. never true
We have:
6 + 8x - 9 = 11x + 14 - 3x
Bring all the terms with x on the left, by subtracting from both sides 11x and -3x, and all the numbers on the right by subtrcting from both sides 6 and -9:
6 + 8x - 9 - 11x - (-3x) - 6 - (-9) = 11x + 14 - 3x - 11x - (-3x) - 6 - (-9)
Cancel out the opposite terms from each side:
8x - 11x + 3x = 14 - 6 + 9
Combine likely terms:
0x = 17
Now you should ask yourself: what number multiplied by zero gives 17 as a result? The answer is none because a number multiplied by zero always equals zero.
Hence, the statement is never true.
C) Answer:
We have:
5r + 4 ≤ 5
Subtract 4 from both sides:
5r + 4 - 4 ≤ 5 - 4
Combine likely terms:
5r ≤ 1
Divide both sides by 5:
To graph the set of solutions, you need to set:
y₁ = 5x + 4 and
y₂ = +5
Plot these two lines:
y₂ is a horizontal line at a height of 5;
y₁ is a line passing through (0, 4) and (1, 9)
The set of solutions will be the part of the graph in which y₁ lies underneath y₂ (see picture attached), that happens for .
Parallel lines should have the same slope. Therefore, you know which point it passes through and the slope. Plug in the points and slop into slope-intercept form to find b. Please refer to the picture.
Unless I am misreading, the question, or don't know all of it, there can be an infinite number of similar shapes. Three are give to you at the bottom of this answer, but there are many more possibilities.
