A is the correct answer “V” (16w)(5w)
The answer is: [C]: " <span>{x | x > 5} " .
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Explanation:
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Given: " 4(x </span>− 3) − 2(x − <span>1) > 0 " ;
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Note the "distributive property of multiplication" :
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a(b+c) = ab + ac ;
a(b</span>−c) = ab −<span> ac ;
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So, given:
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</span> → 4(x − 3) − 2(x − 1) > 0 ;
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Let us simplify; and rewrite:
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Start with:
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</span>→<span> -2 (x </span>− 1) = (-2*x) − (-2 *1) = -2x − (-2) = -2x + 2 ;
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Now, continue with:
</span> → 4(x − 3) = (4*x) − (4*3) = 4x − 12 ;
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</span><span>So, given the original problem:
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</span> → 4(x − 3) − 2(x − 1) > 0 ;
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Rewrite;
Replacing: "4</span>(x − 3)" ; with: "4x − 12" ;
and replacing "− 2(x − 1)" ; with: " -2x + 2" ;
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as follows: </span>→ " 4x − 12 − 2x + 2 " > 0 ;
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On the "left-hand side", combine the "like terms", and simplify ;
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+4x −2x = +2x ; −12 +2 = -10 ; and rewrite:
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</span>→ 2x − 10 > 0 ; Add "10" to EACH SIDE of the inequality;
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</span>→ 2x − 10 + 10 > 0 + 10 ;
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to get: </span>→ 2x > 10 ;
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</span>→<span> Now, divide EACH SIDE of the inequality by "2";
to isolate "x" on one side of the inequality; & to "solve"/"simply" for "x" ;
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</span>→ 2x / 2 > 10 / 2 ;
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</span>→ x > 5 ; which is:
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→ Answer choice: [C]: " {x | x > 5} " .
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Answer: Y = 3x - 2
Work: Okay, let's take this step by step. Since the Y - Intercept is -2, put a dot on -2 on the (Y) Line. It also just so happens that the line goes through -2. Now with 3x. 3x is the same thing as 3x / 1. Since three is on the top, you go up three from -2, and then move over one spot because of the 1 (If it was a negative one, you go the opposite direction) Alright, now you see that the line also passes through that point as well, so it has to be y = 3x -2
<em>I hope this helps, and Happy Holidays! :)</em>
Answer:
Below.
Step-by-step explanation:
4x^2 - 4x - 1 = 0
This will not factor.
But 4x^2 - 4x + 1 = 0 will:
= (2x - 1)(2x - 1) = 0
x = 0.5 (*2)