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Solve 4(x - 3) - 2(x - 1) >0.

{x I x > -5}
{x I x > 5}
{x l x < 5}
{x I x < -5}

2 Answers

1 vote

The answer is: [C]: " x > 5 " .

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Step-by-step explanation:

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Given: " 4(x − 3) − 2(x − 1) > 0 " ;

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Note the "distributive property of multiplication" :

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a(b+c) = ab + ac ;

a(b−c) = ab − ac ;

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So, given:

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→ 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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→ -2 (x − 1) = (-2*x) − (-2 *1) = -2x − (-2) = -2x + 2 ;

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Now, continue with:

→ 4(x − 3) = (4*x) − (4*3) = 4x − 12 ;

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So, given the original problem:

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→ 4(x − 3) − 2(x − 1) > 0 ;

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Rewrite;

Replacing: "4(x − 3)" ; with: "4x − 12" ;

and replacing "− 2(x − 1)" ; with: " -2x + 2" ;

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as follows: → " 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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→ 2x − 10 > 0 ; Add "10" to EACH SIDE of the inequality;

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→ 2x − 10 + 10 > 0 + 10 ;

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to get: → 2x > 10 ;

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→ 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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→ 2x / 2 > 10 / 2 ;

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→ x > 5 ; which is:

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→ Answer choice: [C]: " x > 5 " .

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User Nima Zarei
by
7.6k points
6 votes

Answer:

x >5

Step-by-step explanation:

4(x - 3) - 2(x - 1) >0

Distribute

4x -12 -2x +2 > 0

Combine like terms

2x -10 >0

Add 10 to each side

2x-10+10 > 10

2x>10

Divide each side by 2

2x/2 > 10/2

x >5

User SeanWM
by
8.2k points

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