3(x – 1) < -3(2 – 2x)? A) x > 1 B) x < 1 C) x > -1 D) x < -1

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3(x – 1) < -3(2 – 2x)? A) x > 1 B) x < 1 C) x > -1 D) x < -1

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Answer 1 · 2016-03-27T02:30:07

$B : x < 1$ $"B": x<1$

Explanation:

The given problem is:

$3 (x - 1) < - 3 (2 - 2 x)$ $3(x-1)<-3(2-2x)$

The solutions are:

$A) i x > 1$ $"A")color(white)(i)x>1$
$B) i x < 1$ $"B")color(white)(i)x<1$
$C) i x >$ $"C")color(white)(i)x>$ $- 1$ $-1$
$D) i x < - 1$ $"D")color(white)(i)x<-1$

Solving the Inequality
$1$ $1$ . Start by factoring $- 2$ $-2$ from the bracketed terms on the right-hand side of the equation.

$3 (x - 1) < - 3 (2 - 2 x)$ $3(x-1)<-3(2-2x)$

$3 (x - 1) < - 3 \cdot - 2 (- 1 + x)$ $3(x-1)<-3*-2(-1+x)$

$2$ $2$ . Multiply $- 3$ $-3$ and $- 2$ $-2$ together on the right-hand side of the equation.

$3 (x - 1) < 6 (1 - x)$ $3(x-1)<6(1-x)$

$3$ $3$ . Divide both sides by $6$ $6$ .

$\frac{3 (x - 1)}{6} < \frac{6 (1 - x)}{6}$ $(3(x-1))/6<(6(1-x))/6$

$(color(red)cancelcolor(black)3^1(x-1))/color(red)cancelcolor(black)6^2<(color(red)cancelcolor(black)6^1(1-x))/color(red)cancelcolor(black)6^1$

$(x-1)/2<1-x$

$4$ . Multiply the whole inequality by $2$ to get rid of the denominator.

$2((x-1)/2)<2(1-x)$

$color(red)cancelcolor(black)2^1((x-1)/color(red)cancelcolor(black)2^1)<2(1-x)$

$x-1<2-2x$

$5$ . Add $2x$ to both sides of the equation.

$x$ $color(red)(+2x)-1<2-2x$ $color(red)(+2x)$

$3x-1<2$

$6$ . Add $1$ to both sides of the equation.

$3x-1$ $color(red)(+1)<2$ $color(red)(+1)$

$3x<3$

$7$ . Divide both sides by $3$ .

$(3x)/3<3/3$

$color(green)(|bar(ul(color(white)(a/a)x<1color(white)(a/a)|)))$

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3(x – 1) < -3(2 – 2x)? A) x > 1 B) x < 1 C) x > -1 D) x < -1

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Explanation:

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