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2 years ago

Five fewer than x is at most eighteen. What is the solution set for x?

Mathematics

2 answers:

Colt1911 [192]2 years ago

6 0

Write it out as an equation
x-5 <= 18
Then move the 5 to the other side by adding
x <= 23

natita [175]2 years ago

5 0

X - 5 ≤ 18 , solve for x

Add 5 on both sides
x - 5 + 5 ≤ 18 + 5

Simplify
x ≤ 23

Answer
x ≤ 23

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How many extraneous solutions does the equation below have?

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The given equation consisting of variable , m is

$\frac{2 m}{2 m+3} -\frac{2 m}{2 m-3}=1\\\\ 2 m[\frac{1}{2 m+3} -\frac{1}{2 m-3}]=1\\\\ 2 m\times \frac{[2 m-3 -2 m- 3]}{4m^2-9}=1\\\\ -6 \times 2 m=4 m^2 -9\\\\ 4 m^2 +1 2 m -9=0\\\\m=\frac{-12 \pm\sqrt{12^2-4 \times 4 \times (-9)}}{2\times 4}\\\\m=\frac{-12 \pm \sqrt {144+144}}{8}\\\\m=\frac{-12 \pm \sqrt {288}}{8}\\\\m=\frac{-12 \pm 12 \sqrt{2}}{8}\\\\m=\frac{3}{2}\times(-1 \pm \sqrt{2})$

None of the two solution

$m=\frac{3}{2}\times(-1 +\sqrt{2}) and , m=\frac{3}{2}\times(-1 -\sqrt{2})$ , is extraneous.

Here, L.H.S= R.H.S

Option A: 0→ extraneous

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